®γσ, Eng Lian Hu

Betting Strategy and Ⓜodel Validation - Part II

Betting Strategy and Ⓜodel Validation - Part II

Betting Model Analysis on Sportsbook Consultancy Firm A

®γσ, Eng Lian Hu 白戸則道®

2016-08-23

Abstract

This is an academic research by apply R statistics analysis to an agency A of an existing betting consultancy firm A. According to the Dixon and Pope (2004)1 Kindly refer to 24th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References, due to business confidential and privacy I am also using agency A and firm A in this paper. The purpose of the anaysis is measure the staking model of the firm A. For more sample which using R for Soccer Betting see http://rpubs.com/englianhu. Here is the references of rmarkdown and An Introduction to R Markdown. You are welcome to read the Tony Hirst (2014)2 Kindly refer to 1st paper in Reference for technical research on programming and coding portion for the paper. in 7.4 References if you are getting interest to write a data analysis on Sports-book.

1. Introduction to the Betting Stategics

  • Section [1.1 Introducing Betting Strategies] - Introduce Betting Strategies
  • Section [1.2 Value Betting] - Odds Price and Overrounds Changared by Bookmakers
  • Section [1.3 Professional Gambler] - Punters’ life and How Hedge Fund Works

2. Data

  • Section [2.1 Collect and Reprocess the Data] - Data from Firm A
  • Section [2.2 Overrounds / Vigorish] - Odds Price and Overrounds Changared by Bookmakers

3. Summarise the Staking Model

  • Section [3.1 Summarise Diversified Periodic Stakes] - Summarise the Stakes and Return
  • Section [3.2 Summarise the Staking Handicap] - Summarise the Staking Handicap Breakdown
  • Section [3.3 Summarise the Staking Prices] - Summarise the Staking Price Range Breakdown
  • Section [3.4 Summarise the In-Play Staking Timing] - Summarise the In-Play Staking Breakdown by Time Range
  • Section [3.5 Summarise the In-Play Staking Based on Current Score] - Summarise the In-Play Staking Breakdown by Current Score

4. Staking Ⓜodel

4.1 Basic Equation

Before we start modelling, we look at the summary of investment return rates.

table 4.1.1 : 5 x 5 : Return of annually investment summary table.

\[\Re = \sum_{i=1}^{n}\rho_{i}^{EM}/\sum_{i=1}^{n}\rho_{i}^{BK}\] equation 4.1.1

\(\Re\) is the return rates of investment. The \(\rho_i^{EM}\) is the estimated probabilities which is the calculated by firm A from match 1,2… until \(n\) matches while \(\rho_{i}^{BK}\) is the net/pure probability (real odds) offer by bookmakers after we fit the equation 4.1.2 into equation 4.1.1.

\[\rho_i = P_i^{Lay} / (P_i^{Back} + P_i^{Lay})\] equation 4.1.2

\(P_i^{Back}\) and \(P_i^{Lay}\) is the backed and layed fair price offer by bookmakers.

We can simply apply equation above to get the value \(\Re\). From the table above we know that the EMPrice calculated by firm A invested at a threshold edge (price greater) 1.0769894, 1.1072203, 1.0781056, 1.1148426, 1.0671108 than the prices offer by bookmakers. There are some description about \(\Re\) on Dixon and Coles (1996)3 Kindly refer to 25th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References. The optimal value of \(\rho_{i}\) (rEMProbB) will be calculated based on bootstrapping/resampling method in section 4.3 Kelly Ⓜodel.

table 4.1.2 : 48640 x 45 : Odds price and probabilities sample table.

Above table list a part of sample odds prices and probabilities of soccer match \(i\) while \(n\) indicates the number of soccer matches. We can know the values rEMProbB, netProbB and so forth.


graph 4.1.1 : A sample graph about the relationship between the investmental probabilities -vs- bookmakers’ probabilities.

Graph above shows the probabilities calculated by firm A to back against real probabilities offered by bookmakers over 48640 soccer matches.

Now we look at the result of the soccer matches.

table 4.1.3 : 7 x 8 : Summary of betting results.

The table above summarize the stakes and return on soccer matches result. Well, below table list the handicaps placed by firm A on agency A. I list the handicap prior to test the coefficient according to the handicap in next section 4.2 Linear Ⓜodel.

table 4.1.4 : 6 x 8 : The handicap in sample data.

4.2 Linear Ⓜodel

From our understanding of staking, the covariates we need to consider should be only odds price since the handicap’s covariate has settled according to different handicap of EMOdds.

Again, I don’t pretend to know the correct Ⓜodel, here I simply apply linear model to retrieve the value of EMOdds derived from stakes. The purpose of measure the edge overcame bookmakers’ vigorish is to know the levarage of the staking activities onto 1 unit edge of odds price by firm A to agency A.

Dependent variable:
Return
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
Stakes 1.073*** 1.073*** 1.074*** 1.073*** 1.104*** 1.073*** 1.105*** 1.073*** 1.104*** 1.103*** 1.104***
(0.005) (0.005) (0.005) (0.005) (0.006) (0.005) (0.006) (0.005) (0.006) (0.006) (0.006)
HCap -3.929*** 0.041 0.046 0.112 -13.276***
(0.268) (0.187) (0.187) (0.190) (1.408)
1 | Stakes
netProbB 1.308 1.336 -46.102***
(2.474) (2.477) (4.323)
ipRange(10,15] -1.345 -1.382 -1.397 0.378 0.119 0.199
(1.603) (1.604) (1.618) (1.745) (1.788) (1.860)
ipRange(15,20] -3.400** -3.448** -3.482** -3.296* -3.303* -2.393
(1.614) (1.616) (1.637) (1.796) (1.820) (1.906)
ipRange(20,25] -0.893 -0.943 -0.965 -1.670 -1.596 -2.773
(1.606) (1.609) (1.642) (1.811) (1.814) (1.925)
ipRange(25,30] -3.458** -3.497** -3.496** -3.107* -3.089* -2.378
(1.597) (1.598) (1.639) (1.840) (1.836) (1.956)
ipRange(30,35] -0.248 -0.279 -0.345 -0.579 -0.514 -0.270
(1.604) (1.605) (1.649) (1.866) (1.856) (2.031)
ipRange(35,40] 0.768 0.744 0.585 0.344 0.744 0.689
(1.673) (1.673) (1.723) (1.968) (1.961) (2.199)
ipRange(40,45] 1.104 1.086 1.107 1.937 1.733 2.348
(1.628) (1.628) (1.693) (1.938) (1.918) (2.112)
ipRange(45,50] -0.691 -0.718 -0.749 -0.942 -1.686 -1.349
(1.717) (1.718) (1.788) (2.045) (2.057) (2.211)
ipRange(5,10] -2.206 -2.250* -2.236 -1.237 -1.091 -1.207
(1.361) (1.363) (1.364) (1.453) (1.513) (1.546)
ipRange(50,55] -1.081 -1.104 -1.185 -1.106 -1.286 -0.689
(1.594) (1.595) (1.683) (1.910) (1.896) (2.069)
ipRange(55,60] -1.370 -1.382 -1.457 1.380 1.498 1.623
(1.657) (1.657) (1.757) (2.017) (2.009) (2.210)
ipRange(60,65] -2.567 -2.565 -2.594 -3.261 -3.585 -2.862
(1.861) (1.861) (1.973) (2.271) (2.241) (2.460)
ipRange(65,70] -2.916 -2.895 -2.816 -0.222 -0.948 0.108
(2.035) (2.036) (2.143) (2.551) (2.496) (2.822)
ipRange(70,75] -1.550 -1.520 -1.416 -0.497 -1.418 -0.703
(2.200) (2.201) (2.299) (2.754) (2.795) (3.075)
ipRange(75,80] -1.613 -1.609 -1.432 -1.161 -1.080 1.585
(2.830) (2.830) (2.923) (3.298) (3.373) (3.908)
ipRange(80,85] -4.620 -4.578 -4.786 -6.060 -7.889 -7.715
(5.015) (5.016) (5.098) (5.969) (6.069) (6.798)
ipRange(85,90] -1.661 -1.558 -2.099 -8.572 -7.730 -15.330
(18.711) (18.712) (18.766) (22.265) (25.114) (38.629)
ipRangeET 24.879*** 24.938*** 24.910*** 37.856*** 65.866*** 65.777***
(7.236) (7.237) (7.236) (7.555) (12.674) (12.671)
ipRangeFT 6.061 6.154 7.579 7.473 5.956 5.920
(14.504) (14.505) (14.581) (15.015) (16.368) (16.365)
ipRangeHT 0.076 0.084 0.050 0.524 0.568 1.710
(1.784) (1.784) (1.850) (2.127) (2.098) (2.215)
ipRangeNo -0.428 -0.405 0.488
(0.968) (0.969) (1.132)
CurScore0-1 -0.422 0.770 -0.083 -0.796
(1.158) (1.107) (1.241) (1.403)
CurScore0-2 -3.893 -4.000* -3.621 -6.607**
(2.406) (2.161) (2.473) (2.880)
CurScore0-3 0.502 -0.650 0.565 -1.669
(6.483) (5.528) (6.535) (8.028)
CurScore0-4 -16.514 -12.983 -16.265 5.727
(15.613) (15.580) (15.645) (23.941)
CurScore0-5 -44.559 -42.599 -44.505 10.252
(31.213) (32.392) (31.231) (54.104)
CurScore1-0 0.143 0.366 0.526 -0.040
(1.086) (1.050) (1.165) (1.225)
CurScore1-1 -0.486 0.548 -0.319 0.271
(1.660) (1.418) (1.752) (1.882)
CurScore1-2 -4.001 -3.403 -3.644 -3.406
(2.625) (2.490) (2.741) (3.098)
CurScore1-3 0.620 -0.012 0.461 2.440
(7.178) (6.944) (7.217) (8.505)
CurScore1-4 5.120 1.667 5.154 11.566
(15.000) (15.017) (15.034) (41.404)
CurScore2-0 -0.593 -0.657 -0.536 -0.985
(1.706) (1.712) (1.790) (1.905)
CurScore2-1 4.644 4.516* 4.829 4.436
(3.051) (2.423) (3.130) (3.618)
CurScore2-2 -0.140 4.426 0.224 -1.240
(5.066) (3.728) (5.127) (5.754)
CurScore2-3 -2.597 -4.287 -1.173 -1.548
(8.259) (7.440) (8.356) (10.961)
CurScore2-4 -24.584 -9.231 -24.865 333.433
(31.211) (25.109) (31.286) (376.256)
CurScore3-0 -2.890 -0.715 -2.948 -0.827
(4.304) (4.133) (4.356) (4.897)
CurScore3-1 -0.834 1.025 -0.835 -2.496
(5.920) (5.260) (5.965) (6.862)
CurScore3-2 -1.002 3.105 0.468 21.120
(13.119) (7.450) (13.245) (23.230)
CurScore3-3 -3.374 -11.129 -3.593 -21.715
(16.305) (11.315) (16.355) (26.695)
CurScore3-4 116.118*** 118.017*** 115.350*** 18.330
(38.226) (39.675) (38.250) (54.061)
CurScore4-0 4.294 10.813 4.296 6.441
(16.306) (15.582) (16.336) (20.296)
CurScore4-1 -12.960 -7.582 -12.972 5.930
(14.455) (12.002) (14.480) (31.408)
CurScore4-2 -68.976*** -42.605*** -68.551*** -57.910*
(20.438) (16.224) (20.484) (29.692)
CurScore4-3 16.441 -37.020 16.203 16.333
(54.053) (39.739) (54.086) (54.091)
CurScore5-0 -11.810 -10.748 -11.858 -32.858
(17.106) (17.763) (17.136) (44.518)
CurScore5-1 -56.168 -55.077 -55.559 -56.338
(54.053) (56.083) (54.058) (54.057)
CurScore5-2 -2.725 -0.777 0.008 71.372
(38.225) (39.683) (38.264) (879.489)
CurScore5-3 30.187 31.645 32.979 33.402
(54.054) (56.093) (54.075) (54.076)
CurScoreNo 0.748 -0.396 0.261 0.441
(0.688) (0.969) (1.035) (1.134)
ipHCap:ipRange(10,15] -1.550
(0.963)
ipHCap:ipRange(15,20] -0.566
(0.980)
ipHCap:ipRange(20,25] -0.265
(1.004)
ipHCap:ipRange(25,30] -0.106
(1.053)
ipHCap:ipRange(30,35] -0.020
(1.104)
ipHCap:ipRange(35,40] -0.876
(1.229)
ipHCap:ipRange(40,45] 0.912
(1.238)
ipHCap:ipRange(45,50] 1.920
(1.437)
ipHCap:ipRange(5,10] 0.228
(0.776)
ipHCap:ipRange(50,55] 0.277
(1.409)
ipHCap:ipRange(55,60] -0.680
(1.526)
ipHCap:ipRange(60,65] -0.017
(1.814)
ipHCap:ipRange(65,70] -0.163
(1.995)
ipHCap:ipRange(70,75] 1.012
(2.518)
ipHCap:ipRange(75,80] -1.782
(3.112)
ipHCap:ipRange(80,85] 6.683
(5.753)
ipHCap:ipRange(85,90] -1.643
(15.113)
ipHCap:ipRangeET 56.390***
(20.527)
ipHCap:ipRangeFT -6.888
(28.164)
ipHCap:ipRangeHT 0.770
(1.483)
ipHCap:ipRangeNo 0.461
(0.609)
ipHCap 0.085 0.118 0.128 -0.037 0.425*
(0.170) (0.171) (0.176) (0.552) (0.257)
HCap:netProbB 18.259***
(2.727)
CurScore0-0:ipRange(0,5]:ipHCap -0.541
(0.618)
CurScore0-1:ipRange(0,5]:ipHCap -0.750
(2.848)
CurScore0-2:ipRange(0,5]:ipHCap
CurScore0-3:ipRange(0,5]:ipHCap
CurScore0-4:ipRange(0,5]:ipHCap
CurScore0-5:ipRange(0,5]:ipHCap
CurScore1-0:ipRange(0,5]:ipHCap 2.846
(3.440)
CurScore1-1:ipRange(0,5]:ipHCap 11.383
(14.562)
CurScore1-2:ipRange(0,5]:ipHCap
CurScore1-3:ipRange(0,5]:ipHCap
CurScore1-4:ipRange(0,5]:ipHCap
CurScore2-0:ipRange(0,5]:ipHCap -0.892
(24.166)
CurScore2-1:ipRange(0,5]:ipHCap -2.727
(14.663)
CurScore2-2:ipRange(0,5]:ipHCap 0.628
(8.841)
CurScore2-3:ipRange(0,5]:ipHCap
CurScore2-4:ipRange(0,5]:ipHCap
CurScore3-0:ipRange(0,5]:ipHCap 0.508
(18.087)
CurScore3-1:ipRange(0,5]:ipHCap
CurScore3-2:ipRange(0,5]:ipHCap
CurScore3-3:ipRange(0,5]:ipHCap
CurScore3-4:ipRange(0,5]:ipHCap
CurScore4-0:ipRange(0,5]:ipHCap
CurScore4-1:ipRange(0,5]:ipHCap
CurScore4-2:ipRange(0,5]:ipHCap
CurScore4-3:ipRange(0,5]:ipHCap
CurScore5-0:ipRange(0,5]:ipHCap
CurScore5-1:ipRange(0,5]:ipHCap
CurScore5-2:ipRange(0,5]:ipHCap
CurScore5-3:ipRange(0,5]:ipHCap
CurScoreNo:ipRange(0,5]:ipHCap
CurScore0-0:ipRange(10,15]:ipHCap -1.884*
(1.016)
CurScore0-1:ipRange(10,15]:ipHCap -0.261
(2.523)
CurScore0-2:ipRange(10,15]:ipHCap -11.379*
(6.601)
CurScore0-3:ipRange(10,15]:ipHCap
CurScore0-4:ipRange(10,15]:ipHCap
CurScore0-5:ipRange(10,15]:ipHCap
CurScore1-0:ipRange(10,15]:ipHCap -2.755
(1.964)
CurScore1-1:ipRange(10,15]:ipHCap -1.577
(5.658)
CurScore1-2:ipRange(10,15]:ipHCap -7.195
(11.525)
CurScore1-3:ipRange(10,15]:ipHCap
CurScore1-4:ipRange(10,15]:ipHCap
CurScore2-0:ipRange(10,15]:ipHCap -4.581
(3.960)
CurScore2-1:ipRange(10,15]:ipHCap 12.605
(18.041)
CurScore2-2:ipRange(10,15]:ipHCap
CurScore2-3:ipRange(10,15]:ipHCap
CurScore2-4:ipRange(10,15]:ipHCap
CurScore3-0:ipRange(10,15]:ipHCap 1.179
(10.647)
CurScore3-1:ipRange(10,15]:ipHCap -5.360
(12.285)
CurScore3-2:ipRange(10,15]:ipHCap
CurScore3-3:ipRange(10,15]:ipHCap
CurScore3-4:ipRange(10,15]:ipHCap
CurScore4-0:ipRange(10,15]:ipHCap
CurScore4-1:ipRange(10,15]:ipHCap
CurScore4-2:ipRange(10,15]:ipHCap
CurScore4-3:ipRange(10,15]:ipHCap
CurScore5-0:ipRange(10,15]:ipHCap
CurScore5-1:ipRange(10,15]:ipHCap
CurScore5-2:ipRange(10,15]:ipHCap
CurScore5-3:ipRange(10,15]:ipHCap
CurScoreNo:ipRange(10,15]:ipHCap
CurScore0-0:ipRange(15,20]:ipHCap -1.435
(1.108)
CurScore0-1:ipRange(15,20]:ipHCap 0.174
(2.314)
CurScore0-2:ipRange(15,20]:ipHCap -11.653*
(6.022)
CurScore0-3:ipRange(15,20]:ipHCap
CurScore0-4:ipRange(15,20]:ipHCap
CurScore0-5:ipRange(15,20]:ipHCap
CurScore1-0:ipRange(15,20]:ipHCap -1.722
(1.832)
CurScore1-1:ipRange(15,20]:ipHCap 12.917***
(4.669)
CurScore1-2:ipRange(15,20]:ipHCap -27.477
(17.680)
CurScore1-3:ipRange(15,20]:ipHCap
CurScore1-4:ipRange(15,20]:ipHCap
CurScore2-0:ipRange(15,20]:ipHCap 1.659
(3.783)
CurScore2-1:ipRange(15,20]:ipHCap 0.932
(10.468)
CurScore2-2:ipRange(15,20]:ipHCap
CurScore2-3:ipRange(15,20]:ipHCap
CurScore2-4:ipRange(15,20]:ipHCap
CurScore3-0:ipRange(15,20]:ipHCap -22.553**
(10.703)
CurScore3-1:ipRange(15,20]:ipHCap
CurScore3-2:ipRange(15,20]:ipHCap
CurScore3-3:ipRange(15,20]:ipHCap
CurScore3-4:ipRange(15,20]:ipHCap
CurScore4-0:ipRange(15,20]:ipHCap
CurScore4-1:ipRange(15,20]:ipHCap
CurScore4-2:ipRange(15,20]:ipHCap
CurScore4-3:ipRange(15,20]:ipHCap
CurScore5-0:ipRange(15,20]:ipHCap
CurScore5-1:ipRange(15,20]:ipHCap
CurScore5-2:ipRange(15,20]:ipHCap
CurScore5-3:ipRange(15,20]:ipHCap
CurScoreNo:ipRange(15,20]:ipHCap
CurScore0-0:ipRange(20,25]:ipHCap 2.148
(1.313)
CurScore0-1:ipRange(20,25]:ipHCap -5.568**
(2.234)
CurScore0-2:ipRange(20,25]:ipHCap -8.052*
(4.854)
CurScore0-3:ipRange(20,25]:ipHCap -34.024
(27.320)
CurScore0-4:ipRange(20,25]:ipHCap
CurScore0-5:ipRange(20,25]:ipHCap
CurScore1-0:ipRange(20,25]:ipHCap -1.275
(1.680)
CurScore1-1:ipRange(20,25]:ipHCap -4.965
(3.589)
CurScore1-2:ipRange(20,25]:ipHCap -10.877
(16.984)
CurScore1-3:ipRange(20,25]:ipHCap
CurScore1-4:ipRange(20,25]:ipHCap
CurScore2-0:ipRange(20,25]:ipHCap -0.547
(3.406)
CurScore2-1:ipRange(20,25]:ipHCap -4.834
(7.109)
CurScore2-2:ipRange(20,25]:ipHCap
CurScore2-3:ipRange(20,25]:ipHCap
CurScore2-4:ipRange(20,25]:ipHCap
CurScore3-0:ipRange(20,25]:ipHCap 24.363
(24.120)
CurScore3-1:ipRange(20,25]:ipHCap
CurScore3-2:ipRange(20,25]:ipHCap
CurScore3-3:ipRange(20,25]:ipHCap
CurScore3-4:ipRange(20,25]:ipHCap
CurScore4-0:ipRange(20,25]:ipHCap
CurScore4-1:ipRange(20,25]:ipHCap
CurScore4-2:ipRange(20,25]:ipHCap
CurScore4-3:ipRange(20,25]:ipHCap
CurScore5-0:ipRange(20,25]:ipHCap
CurScore5-1:ipRange(20,25]:ipHCap
CurScore5-2:ipRange(20,25]:ipHCap
CurScore5-3:ipRange(20,25]:ipHCap
CurScoreNo:ipRange(20,25]:ipHCap
CurScore0-0:ipRange(25,30]:ipHCap -1.387
(1.416)
CurScore0-1:ipRange(25,30]:ipHCap -3.014
(2.562)
CurScore0-2:ipRange(25,30]:ipHCap 3.713
(3.972)
CurScore0-3:ipRange(25,30]:ipHCap
CurScore0-4:ipRange(25,30]:ipHCap
CurScore0-5:ipRange(25,30]:ipHCap
CurScore1-0:ipRange(25,30]:ipHCap 1.781
(1.864)
CurScore1-1:ipRange(25,30]:ipHCap 4.122
(3.752)
CurScore1-2:ipRange(25,30]:ipHCap 30.417**
(15.013)
CurScore1-3:ipRange(25,30]:ipHCap
CurScore1-4:ipRange(25,30]:ipHCap
CurScore2-0:ipRange(25,30]:ipHCap -6.481**
(3.257)
CurScore2-1:ipRange(25,30]:ipHCap -3.673
(10.754)
CurScore2-2:ipRange(25,30]:ipHCap -61.890
(217.400)
CurScore2-3:ipRange(25,30]:ipHCap
CurScore2-4:ipRange(25,30]:ipHCap
CurScore3-0:ipRange(25,30]:ipHCap -13.122
(10.690)
CurScore3-1:ipRange(25,30]:ipHCap -14.946
(12.207)
CurScore3-2:ipRange(25,30]:ipHCap
CurScore3-3:ipRange(25,30]:ipHCap
CurScore3-4:ipRange(25,30]:ipHCap
CurScore4-0:ipRange(25,30]:ipHCap
CurScore4-1:ipRange(25,30]:ipHCap
CurScore4-2:ipRange(25,30]:ipHCap
CurScore4-3:ipRange(25,30]:ipHCap
CurScore5-0:ipRange(25,30]:ipHCap
CurScore5-1:ipRange(25,30]:ipHCap
CurScore5-2:ipRange(25,30]:ipHCap
CurScore5-3:ipRange(25,30]:ipHCap
CurScoreNo:ipRange(25,30]:ipHCap
CurScore0-0:ipRange(30,35]:ipHCap -0.316
(1.594)
CurScore0-1:ipRange(30,35]:ipHCap -1.186
(2.770)
CurScore0-2:ipRange(30,35]:ipHCap -1.367
(5.479)
CurScore0-3:ipRange(30,35]:ipHCap
CurScore0-4:ipRange(30,35]:ipHCap
CurScore0-5:ipRange(30,35]:ipHCap
CurScore1-0:ipRange(30,35]:ipHCap -2.002
(2.142)
CurScore1-1:ipRange(30,35]:ipHCap 6.900
(4.488)
CurScore1-2:ipRange(30,35]:ipHCap -7.334
(11.609)
CurScore1-3:ipRange(30,35]:ipHCap 16.026
(18.363)
CurScore1-4:ipRange(30,35]:ipHCap -3.434
(26.450)
CurScore2-0:ipRange(30,35]:ipHCap 0.760
(2.867)
CurScore2-1:ipRange(30,35]:ipHCap -6.608
(8.579)
CurScore2-2:ipRange(30,35]:ipHCap -5.782
(22.412)
CurScore2-3:ipRange(30,35]:ipHCap
CurScore2-4:ipRange(30,35]:ipHCap
CurScore3-0:ipRange(30,35]:ipHCap -2.435
(4.796)
CurScore3-1:ipRange(30,35]:ipHCap 0.205
(13.659)
CurScore3-2:ipRange(30,35]:ipHCap
CurScore3-3:ipRange(30,35]:ipHCap
CurScore3-4:ipRange(30,35]:ipHCap
CurScore4-0:ipRange(30,35]:ipHCap
CurScore4-1:ipRange(30,35]:ipHCap
CurScore4-2:ipRange(30,35]:ipHCap
CurScore4-3:ipRange(30,35]:ipHCap
CurScore5-0:ipRange(30,35]:ipHCap
CurScore5-1:ipRange(30,35]:ipHCap
CurScore5-2:ipRange(30,35]:ipHCap
CurScore5-3:ipRange(30,35]:ipHCap
CurScoreNo:ipRange(30,35]:ipHCap
CurScore0-0:ipRange(35,40]:ipHCap -2.845
(1.907)
CurScore0-1:ipRange(35,40]:ipHCap 2.126
(3.049)
CurScore0-2:ipRange(35,40]:ipHCap -5.570
(4.797)
CurScore0-3:ipRange(35,40]:ipHCap 52.776***
(16.297)
CurScore0-4:ipRange(35,40]:ipHCap
CurScore0-5:ipRange(35,40]:ipHCap
CurScore1-0:ipRange(35,40]:ipHCap 1.241
(2.425)
CurScore1-1:ipRange(35,40]:ipHCap -12.267**
(5.120)
CurScore1-2:ipRange(35,40]:ipHCap -4.018
(14.542)
CurScore1-3:ipRange(35,40]:ipHCap 6.946
(17.719)
CurScore1-4:ipRange(35,40]:ipHCap
CurScore2-0:ipRange(35,40]:ipHCap -0.573
(3.359)
CurScore2-1:ipRange(35,40]:ipHCap -6.833
(9.757)
CurScore2-2:ipRange(35,40]:ipHCap -51.297**
(23.727)
CurScore2-3:ipRange(35,40]:ipHCap -98.935
(220.607)
CurScore2-4:ipRange(35,40]:ipHCap
CurScore3-0:ipRange(35,40]:ipHCap -3.945
(6.223)
CurScore3-1:ipRange(35,40]:ipHCap 7.773
(14.746)
CurScore3-2:ipRange(35,40]:ipHCap
CurScore3-3:ipRange(35,40]:ipHCap
CurScore3-4:ipRange(35,40]:ipHCap 773.972**
(305.653)
CurScore4-0:ipRange(35,40]:ipHCap
CurScore4-1:ipRange(35,40]:ipHCap 24.860
(17.632)
CurScore4-2:ipRange(35,40]:ipHCap
CurScore4-3:ipRange(35,40]:ipHCap
CurScore5-0:ipRange(35,40]:ipHCap
CurScore5-1:ipRange(35,40]:ipHCap
CurScore5-2:ipRange(35,40]:ipHCap
CurScore5-3:ipRange(35,40]:ipHCap
CurScoreNo:ipRange(35,40]:ipHCap
CurScore0-0:ipRange(40,45]:ipHCap -0.086
(2.137)
CurScore0-1:ipRange(40,45]:ipHCap -0.270
(3.294)
CurScore0-2:ipRange(40,45]:ipHCap -3.425
(4.670)
CurScore0-3:ipRange(40,45]:ipHCap -16.908
(11.199)
CurScore0-4:ipRange(40,45]:ipHCap
CurScore0-5:ipRange(40,45]:ipHCap
CurScore1-0:ipRange(40,45]:ipHCap 0.191
(2.486)
CurScore1-1:ipRange(40,45]:ipHCap 7.403
(4.692)
CurScore1-2:ipRange(40,45]:ipHCap -7.092
(9.390)
CurScore1-3:ipRange(40,45]:ipHCap 10.691
(14.227)
CurScore1-4:ipRange(40,45]:ipHCap
CurScore2-0:ipRange(40,45]:ipHCap 2.449
(2.594)
CurScore2-1:ipRange(40,45]:ipHCap -3.913
(6.997)
CurScore2-2:ipRange(40,45]:ipHCap 23.138
(22.777)
CurScore2-3:ipRange(40,45]:ipHCap
CurScore2-4:ipRange(40,45]:ipHCap
CurScore3-0:ipRange(40,45]:ipHCap 0.597
(5.604)
CurScore3-1:ipRange(40,45]:ipHCap -7.985
(13.112)
CurScore3-2:ipRange(40,45]:ipHCap 57.280
(47.062)
CurScore3-3:ipRange(40,45]:ipHCap
CurScore3-4:ipRange(40,45]:ipHCap
CurScore4-0:ipRange(40,45]:ipHCap
CurScore4-1:ipRange(40,45]:ipHCap
CurScore4-2:ipRange(40,45]:ipHCap
CurScore4-3:ipRange(40,45]:ipHCap
CurScore5-0:ipRange(40,45]:ipHCap
CurScore5-1:ipRange(40,45]:ipHCap
CurScore5-2:ipRange(40,45]:ipHCap
CurScore5-3:ipRange(40,45]:ipHCap
CurScoreNo:ipRange(40,45]:ipHCap
CurScore0-0:ipRange(45,50]:ipHCap -0.022
(2.635)
CurScore0-1:ipRange(45,50]:ipHCap 0.055
(3.509)
CurScore0-2:ipRange(45,50]:ipHCap -2.063
(6.397)
CurScore0-3:ipRange(45,50]:ipHCap 2.606
(9.210)
CurScore0-4:ipRange(45,50]:ipHCap -6.243
(17.163)
CurScore0-5:ipRange(45,50]:ipHCap -100.170**
(43.704)
CurScore1-0:ipRange(45,50]:ipHCap 6.463**
(2.843)
CurScore1-1:ipRange(45,50]:ipHCap -3.453
(6.440)
CurScore1-2:ipRange(45,50]:ipHCap 6.258
(7.259)
CurScore1-3:ipRange(45,50]:ipHCap 4.935
(12.586)
CurScore1-4:ipRange(45,50]:ipHCap
CurScore2-0:ipRange(45,50]:ipHCap 1.415
(3.430)
CurScore2-1:ipRange(45,50]:ipHCap 0.481
(7.099)
CurScore2-2:ipRange(45,50]:ipHCap -9.329
(11.437)
CurScore2-3:ipRange(45,50]:ipHCap -23.221
(35.126)
CurScore2-4:ipRange(45,50]:ipHCap
CurScore3-0:ipRange(45,50]:ipHCap -0.315
(5.928)
CurScore3-1:ipRange(45,50]:ipHCap 27.191
(16.695)
CurScore3-2:ipRange(45,50]:ipHCap
CurScore3-3:ipRange(45,50]:ipHCap 30.378
(34.449)
CurScore3-4:ipRange(45,50]:ipHCap
CurScore4-0:ipRange(45,50]:ipHCap
CurScore4-1:ipRange(45,50]:ipHCap 5.035
(32.362)
CurScore4-2:ipRange(45,50]:ipHCap
CurScore4-3:ipRange(45,50]:ipHCap
CurScore5-0:ipRange(45,50]:ipHCap -0.487
(40.015)
CurScore5-1:ipRange(45,50]:ipHCap
CurScore5-2:ipRange(45,50]:ipHCap
CurScore5-3:ipRange(45,50]:ipHCap
CurScoreNo:ipRange(45,50]:ipHCap
CurScore0-0:ipRange(5,10]:ipHCap -0.241
(0.657)
CurScore0-1:ipRange(5,10]:ipHCap -0.998
(2.070)
CurScore0-2:ipRange(5,10]:ipHCap -4.396
(8.056)
CurScore0-3:ipRange(5,10]:ipHCap
CurScore0-4:ipRange(5,10]:ipHCap
CurScore0-5:ipRange(5,10]:ipHCap
CurScore1-0:ipRange(5,10]:ipHCap 0.687
(1.927)
CurScore1-1:ipRange(5,10]:ipHCap 3.409
(6.132)
CurScore1-2:ipRange(5,10]:ipHCap -30.537
(33.873)
CurScore1-3:ipRange(5,10]:ipHCap
CurScore1-4:ipRange(5,10]:ipHCap
CurScore2-0:ipRange(5,10]:ipHCap -6.595
(6.042)
CurScore2-1:ipRange(5,10]:ipHCap
CurScore2-2:ipRange(5,10]:ipHCap
CurScore2-3:ipRange(5,10]:ipHCap
CurScore2-4:ipRange(5,10]:ipHCap
CurScore3-0:ipRange(5,10]:ipHCap
CurScore3-1:ipRange(5,10]:ipHCap
CurScore3-2:ipRange(5,10]:ipHCap
CurScore3-3:ipRange(5,10]:ipHCap
CurScore3-4:ipRange(5,10]:ipHCap
CurScore4-0:ipRange(5,10]:ipHCap
CurScore4-1:ipRange(5,10]:ipHCap
CurScore4-2:ipRange(5,10]:ipHCap
CurScore4-3:ipRange(5,10]:ipHCap
CurScore5-0:ipRange(5,10]:ipHCap
CurScore5-1:ipRange(5,10]:ipHCap
CurScore5-2:ipRange(5,10]:ipHCap
CurScore5-3:ipRange(5,10]:ipHCap
CurScoreNo:ipRange(5,10]:ipHCap
CurScore0-0:ipRange(50,55]:ipHCap -0.841
(2.911)
CurScore0-1:ipRange(50,55]:ipHCap 0.024
(3.511)
CurScore0-2:ipRange(50,55]:ipHCap 6.528
(4.687)
CurScore0-3:ipRange(50,55]:ipHCap 14.313
(14.023)
CurScore0-4:ipRange(50,55]:ipHCap -1.250
(19.705)
CurScore0-5:ipRange(50,55]:ipHCap
CurScore1-0:ipRange(50,55]:ipHCap 2.376
(2.519)
CurScore1-1:ipRange(50,55]:ipHCap -4.367
(5.350)
CurScore1-2:ipRange(50,55]:ipHCap -11.179
(6.886)
CurScore1-3:ipRange(50,55]:ipHCap 12.687
(16.930)
CurScore1-4:ipRange(50,55]:ipHCap 18.748
(27.234)
CurScore2-0:ipRange(50,55]:ipHCap -6.512**
(3.204)
CurScore2-1:ipRange(50,55]:ipHCap 0.250
(6.869)
CurScore2-2:ipRange(50,55]:ipHCap 1.121
(16.832)
CurScore2-3:ipRange(50,55]:ipHCap -24.250
(40.159)
CurScore2-4:ipRange(50,55]:ipHCap
CurScore3-0:ipRange(50,55]:ipHCap 18.328**
(7.885)
CurScore3-1:ipRange(50,55]:ipHCap 6.435
(11.965)
CurScore3-2:ipRange(50,55]:ipHCap
CurScore3-3:ipRange(50,55]:ipHCap
CurScore3-4:ipRange(50,55]:ipHCap
CurScore4-0:ipRange(50,55]:ipHCap -9.013
(22.691)
CurScore4-1:ipRange(50,55]:ipHCap -21.524
(18.651)
CurScore4-2:ipRange(50,55]:ipHCap
CurScore4-3:ipRange(50,55]:ipHCap
CurScore5-0:ipRange(50,55]:ipHCap
CurScore5-1:ipRange(50,55]:ipHCap
CurScore5-2:ipRange(50,55]:ipHCap
CurScore5-3:ipRange(50,55]:ipHCap
CurScoreNo:ipRange(50,55]:ipHCap
CurScore0-0:ipRange(55,60]:ipHCap -5.170
(4.146)
CurScore0-1:ipRange(55,60]:ipHCap 2.936
(3.913)
CurScore0-2:ipRange(55,60]:ipHCap -1.121
(5.273)
CurScore0-3:ipRange(55,60]:ipHCap -0.411
(7.316)
CurScore0-4:ipRange(55,60]:ipHCap 14.345
(47.291)
CurScore0-5:ipRange(55,60]:ipHCap
CurScore1-0:ipRange(55,60]:ipHCap 2.536
(3.260)
CurScore1-1:ipRange(55,60]:ipHCap -1.570
(5.497)
CurScore1-2:ipRange(55,60]:ipHCap -3.040
(7.391)
CurScore1-3:ipRange(55,60]:ipHCap 1.535
(13.070)
CurScore1-4:ipRange(55,60]:ipHCap -8.073
(17.924)
CurScore2-0:ipRange(55,60]:ipHCap 0.192
(3.284)
CurScore2-1:ipRange(55,60]:ipHCap -5.277
(8.315)
CurScore2-2:ipRange(55,60]:ipHCap -5.275
(13.510)
CurScore2-3:ipRange(55,60]:ipHCap -296.915
(220.595)
CurScore2-4:ipRange(55,60]:ipHCap
CurScore3-0:ipRange(55,60]:ipHCap -3.005
(4.224)
CurScore3-1:ipRange(55,60]:ipHCap -13.620
(12.799)
CurScore3-2:ipRange(55,60]:ipHCap -3.334
(32.368)
CurScore3-3:ipRange(55,60]:ipHCap -338.794
(241.137)
CurScore3-4:ipRange(55,60]:ipHCap
CurScore4-0:ipRange(55,60]:ipHCap
CurScore4-1:ipRange(55,60]:ipHCap -81.512
(50.015)
CurScore4-2:ipRange(55,60]:ipHCap
CurScore4-3:ipRange(55,60]:ipHCap
CurScore5-0:ipRange(55,60]:ipHCap 5.485
(13.942)
CurScore5-1:ipRange(55,60]:ipHCap
CurScore5-2:ipRange(55,60]:ipHCap
CurScore5-3:ipRange(55,60]:ipHCap
CurScoreNo:ipRange(55,60]:ipHCap
CurScore0-0:ipRange(60,65]:ipHCap 6.807
(6.499)
CurScore0-1:ipRange(60,65]:ipHCap -0.287
(4.778)
CurScore0-2:ipRange(60,65]:ipHCap 6.476
(5.475)
CurScore0-3:ipRange(60,65]:ipHCap -6.089
(9.309)
CurScore0-4:ipRange(60,65]:ipHCap -53.309***
(15.769)
CurScore0-5:ipRange(60,65]:ipHCap
CurScore1-0:ipRange(60,65]:ipHCap 2.687
(4.269)
CurScore1-1:ipRange(60,65]:ipHCap 14.808*
(8.538)
CurScore1-2:ipRange(60,65]:ipHCap -10.842
(7.088)
CurScore1-3:ipRange(60,65]:ipHCap 6.935
(12.829)
CurScore1-4:ipRange(60,65]:ipHCap 0.395
(29.960)
CurScore2-0:ipRange(60,65]:ipHCap -0.556
(4.447)
CurScore2-1:ipRange(60,65]:ipHCap -19.695*
(10.081)
CurScore2-2:ipRange(60,65]:ipHCap 4.783
(14.328)
CurScore2-3:ipRange(60,65]:ipHCap 6.482
(24.694)
CurScore2-4:ipRange(60,65]:ipHCap
CurScore3-0:ipRange(60,65]:ipHCap -0.909
(4.713)
CurScore3-1:ipRange(60,65]:ipHCap -9.467
(9.104)
CurScore3-2:ipRange(60,65]:ipHCap -38.391
(35.677)
CurScore3-3:ipRange(60,65]:ipHCap
CurScore3-4:ipRange(60,65]:ipHCap
CurScore4-0:ipRange(60,65]:ipHCap 4.115
(15.401)
CurScore4-1:ipRange(60,65]:ipHCap
CurScore4-2:ipRange(60,65]:ipHCap -47.412
(61.675)
CurScore4-3:ipRange(60,65]:ipHCap
CurScore5-0:ipRange(60,65]:ipHCap 21.431
(42.410)
CurScore5-1:ipRange(60,65]:ipHCap
CurScore5-2:ipRange(60,65]:ipHCap -25.231
(305.620)
CurScore5-3:ipRange(60,65]:ipHCap
CurScoreNo:ipRange(60,65]:ipHCap
CurScore0-0:ipRange(65,70]:ipHCap 0.992
(10.328)
CurScore0-1:ipRange(65,70]:ipHCap 1.546
(6.139)
CurScore0-2:ipRange(65,70]:ipHCap -0.627
(6.256)
CurScore0-3:ipRange(65,70]:ipHCap -7.673
(8.132)
CurScore0-4:ipRange(65,70]:ipHCap -9.911
(8.313)
CurScore0-5:ipRange(65,70]:ipHCap 1.998
(16.106)
CurScore1-0:ipRange(65,70]:ipHCap -2.290
(5.515)
CurScore1-1:ipRange(65,70]:ipHCap -1.934
(13.745)
CurScore1-2:ipRange(65,70]:ipHCap 1.848
(10.325)
CurScore1-3:ipRange(65,70]:ipHCap 8.040
(12.713)
CurScore1-4:ipRange(65,70]:ipHCap 23.734
(22.703)
CurScore2-0:ipRange(65,70]:ipHCap 2.785
(4.383)
CurScore2-1:ipRange(65,70]:ipHCap -3.303
(9.345)
CurScore2-2:ipRange(65,70]:ipHCap 2.580
(18.880)
CurScore2-3:ipRange(65,70]:ipHCap 39.679
(25.955)
CurScore2-4:ipRange(65,70]:ipHCap -253.388
(264.672)
CurScore3-0:ipRange(65,70]:ipHCap -10.159*
(5.658)
CurScore3-1:ipRange(65,70]:ipHCap 11.591
(9.112)
CurScore3-2:ipRange(65,70]:ipHCap -16.139
(27.905)
CurScore3-3:ipRange(65,70]:ipHCap 52.923
(113.401)
CurScore3-4:ipRange(65,70]:ipHCap
CurScore4-0:ipRange(65,70]:ipHCap
CurScore4-1:ipRange(65,70]:ipHCap 2.368
(12.737)
CurScore4-2:ipRange(65,70]:ipHCap -5.721
(20.488)
CurScore4-3:ipRange(65,70]:ipHCap
CurScore5-0:ipRange(65,70]:ipHCap
CurScore5-1:ipRange(65,70]:ipHCap
CurScore5-2:ipRange(65,70]:ipHCap
CurScore5-3:ipRange(65,70]:ipHCap
CurScoreNo:ipRange(65,70]:ipHCap
CurScore0-0:ipRange(70,75]:ipHCap -4.554
(12.525)
CurScore0-1:ipRange(70,75]:ipHCap 9.464
(7.352)
CurScore0-2:ipRange(70,75]:ipHCap 7.281
(7.567)
CurScore0-3:ipRange(70,75]:ipHCap 3.774
(9.384)
CurScore0-4:ipRange(70,75]:ipHCap -22.581
(15.949)
CurScore0-5:ipRange(70,75]:ipHCap
CurScore1-0:ipRange(70,75]:ipHCap 4.288
(6.919)
CurScore1-1:ipRange(70,75]:ipHCap -1.833
(18.122)
CurScore1-2:ipRange(70,75]:ipHCap 0.540
(10.205)
CurScore1-3:ipRange(70,75]:ipHCap -1.275
(11.367)
CurScore1-4:ipRange(70,75]:ipHCap
CurScore2-0:ipRange(70,75]:ipHCap -3.597
(5.051)
CurScore2-1:ipRange(70,75]:ipHCap -3.879
(12.897)
CurScore2-2:ipRange(70,75]:ipHCap -18.499
(37.808)
CurScore2-3:ipRange(70,75]:ipHCap -0.315
(29.367)
CurScore2-4:ipRange(70,75]:ipHCap
CurScore3-0:ipRange(70,75]:ipHCap -8.169
(10.255)
CurScore3-1:ipRange(70,75]:ipHCap -6.751
(10.983)
CurScore3-2:ipRange(70,75]:ipHCap
CurScore3-3:ipRange(70,75]:ipHCap
CurScore3-4:ipRange(70,75]:ipHCap
CurScore4-0:ipRange(70,75]:ipHCap 1.690
(14.446)
CurScore4-1:ipRange(70,75]:ipHCap
CurScore4-2:ipRange(70,75]:ipHCap 34.299
(24.117)
CurScore4-3:ipRange(70,75]:ipHCap
CurScore5-0:ipRange(70,75]:ipHCap 5.852
(14.013)
CurScore5-1:ipRange(70,75]:ipHCap
CurScore5-2:ipRange(70,75]:ipHCap
CurScore5-3:ipRange(70,75]:ipHCap
CurScoreNo:ipRange(70,75]:ipHCap
CurScore0-0:ipRange(75,80]:ipHCap 7.096
(13.860)
CurScore0-1:ipRange(75,80]:ipHCap -8.723
(9.054)
CurScore0-2:ipRange(75,80]:ipHCap 2.407
(8.287)
CurScore0-3:ipRange(75,80]:ipHCap -4.170
(9.160)
CurScore0-4:ipRange(75,80]:ipHCap 8.761
(9.554)
CurScore0-5:ipRange(75,80]:ipHCap
CurScore1-0:ipRange(75,80]:ipHCap -12.554
(10.867)
CurScore1-1:ipRange(75,80]:ipHCap -18.827
(22.290)
CurScore1-2:ipRange(75,80]:ipHCap -3.852
(12.349)
CurScore1-3:ipRange(75,80]:ipHCap -9.532
(26.800)
CurScore1-4:ipRange(75,80]:ipHCap -0.372
(16.476)
CurScore2-0:ipRange(75,80]:ipHCap -3.444
(8.985)
CurScore2-1:ipRange(75,80]:ipHCap -13.530
(21.801)
CurScore2-2:ipRange(75,80]:ipHCap 17.045
(81.769)
CurScore2-3:ipRange(75,80]:ipHCap -35.891
(32.238)
CurScore2-4:ipRange(75,80]:ipHCap
CurScore3-0:ipRange(75,80]:ipHCap -0.891
(12.737)
CurScore3-1:ipRange(75,80]:ipHCap -1.369
(27.290)
CurScore3-2:ipRange(75,80]:ipHCap 19.026
(35.327)
CurScore3-3:ipRange(75,80]:ipHCap 198.411**
(98.959)
CurScore3-4:ipRange(75,80]:ipHCap
CurScore4-0:ipRange(75,80]:ipHCap -82.902
(115.652)
CurScore4-1:ipRange(75,80]:ipHCap -6.051
(21.396)
CurScore4-2:ipRange(75,80]:ipHCap -183.762
(123.496)
CurScore4-3:ipRange(75,80]:ipHCap
CurScore5-0:ipRange(75,80]:ipHCap 6.957
(14.646)
CurScore5-1:ipRange(75,80]:ipHCap
CurScore5-2:ipRange(75,80]:ipHCap
CurScore5-3:ipRange(75,80]:ipHCap
CurScoreNo:ipRange(75,80]:ipHCap
CurScore0-0:ipRange(80,85]:ipHCap 2.782
(53.571)
CurScore0-1:ipRange(80,85]:ipHCap -0.919
(12.153)
CurScore0-2:ipRange(80,85]:ipHCap 16.258
(12.394)
CurScore0-3:ipRange(80,85]:ipHCap 21.735
(13.726)
CurScore0-4:ipRange(80,85]:ipHCap
CurScore0-5:ipRange(80,85]:ipHCap
CurScore1-0:ipRange(80,85]:ipHCap 7.503
(25.362)
CurScore1-1:ipRange(80,85]:ipHCap 48.943
(155.239)
CurScore1-2:ipRange(80,85]:ipHCap 6.740
(22.324)
CurScore1-3:ipRange(80,85]:ipHCap
CurScore1-4:ipRange(80,85]:ipHCap
CurScore2-0:ipRange(80,85]:ipHCap 1.870
(18.971)
CurScore2-1:ipRange(80,85]:ipHCap 0.796
(26.018)
CurScore2-2:ipRange(80,85]:ipHCap -22.450
(109.427)
CurScore2-3:ipRange(80,85]:ipHCap 10.479
(28.601)
CurScore2-4:ipRange(80,85]:ipHCap
CurScore3-0:ipRange(80,85]:ipHCap -20.154
(17.902)
CurScore3-1:ipRange(80,85]:ipHCap
CurScore3-2:ipRange(80,85]:ipHCap -43.277
(70.491)
CurScore3-3:ipRange(80,85]:ipHCap
CurScore3-4:ipRange(80,85]:ipHCap
CurScore4-0:ipRange(80,85]:ipHCap
CurScore4-1:ipRange(80,85]:ipHCap
CurScore4-2:ipRange(80,85]:ipHCap
CurScore4-3:ipRange(80,85]:ipHCap
CurScore5-0:ipRange(80,85]:ipHCap
CurScore5-1:ipRange(80,85]:ipHCap
CurScore5-2:ipRange(80,85]:ipHCap
CurScore5-3:ipRange(80,85]:ipHCap
CurScoreNo:ipRange(80,85]:ipHCap
CurScore0-0:ipRange(85,90]:ipHCap
CurScore0-1:ipRange(85,90]:ipHCap -14.376
(43.660)
CurScore0-2:ipRange(85,90]:ipHCap
CurScore0-3:ipRange(85,90]:ipHCap
CurScore0-4:ipRange(85,90]:ipHCap
CurScore0-5:ipRange(85,90]:ipHCap
CurScore1-0:ipRange(85,90]:ipHCap
CurScore1-1:ipRange(85,90]:ipHCap
CurScore1-2:ipRange(85,90]:ipHCap
CurScore1-3:ipRange(85,90]:ipHCap
CurScore1-4:ipRange(85,90]:ipHCap
CurScore2-0:ipRange(85,90]:ipHCap 7.267
(33.214)
CurScore2-1:ipRange(85,90]:ipHCap
CurScore2-2:ipRange(85,90]:ipHCap
CurScore2-3:ipRange(85,90]:ipHCap -10.774
(67.294)
CurScore2-4:ipRange(85,90]:ipHCap
CurScore3-0:ipRange(85,90]:ipHCap -0.602
(22.196)
CurScore3-1:ipRange(85,90]:ipHCap
CurScore3-2:ipRange(85,90]:ipHCap -7.975
(70.342)
CurScore3-3:ipRange(85,90]:ipHCap
CurScore3-4:ipRange(85,90]:ipHCap
CurScore4-0:ipRange(85,90]:ipHCap
CurScore4-1:ipRange(85,90]:ipHCap
CurScore4-2:ipRange(85,90]:ipHCap
CurScore4-3:ipRange(85,90]:ipHCap
CurScore5-0:ipRange(85,90]:ipHCap
CurScore5-1:ipRange(85,90]:ipHCap
CurScore5-2:ipRange(85,90]:ipHCap
CurScore5-3:ipRange(85,90]:ipHCap
CurScoreNo:ipRange(85,90]:ipHCap
CurScore0-0:ipRangeET:ipHCap 55.898***
(20.517)
CurScore0-1:ipRangeET:ipHCap
CurScore0-2:ipRangeET:ipHCap
CurScore0-3:ipRangeET:ipHCap
CurScore0-4:ipRangeET:ipHCap
CurScore0-5:ipRangeET:ipHCap
CurScore1-0:ipRangeET:ipHCap
CurScore1-1:ipRangeET:ipHCap
CurScore1-2:ipRangeET:ipHCap
CurScore1-3:ipRangeET:ipHCap
CurScore1-4:ipRangeET:ipHCap
CurScore2-0:ipRangeET:ipHCap
CurScore2-1:ipRangeET:ipHCap
CurScore2-2:ipRangeET:ipHCap
CurScore2-3:ipRangeET:ipHCap
CurScore2-4:ipRangeET:ipHCap
CurScore3-0:ipRangeET:ipHCap
CurScore3-1:ipRangeET:ipHCap
CurScore3-2:ipRangeET:ipHCap
CurScore3-3:ipRangeET:ipHCap
CurScore3-4:ipRangeET:ipHCap
CurScore4-0:ipRangeET:ipHCap
CurScore4-1:ipRangeET:ipHCap
CurScore4-2:ipRangeET:ipHCap
CurScore4-3:ipRangeET:ipHCap
CurScore5-0:ipRangeET:ipHCap
CurScore5-1:ipRangeET:ipHCap
CurScore5-2:ipRangeET:ipHCap
CurScore5-3:ipRangeET:ipHCap
CurScoreNo:ipRangeET:ipHCap
CurScore0-0:ipRangeFT:ipHCap -7.354
(28.154)
CurScore0-1:ipRangeFT:ipHCap
CurScore0-2:ipRangeFT:ipHCap
CurScore0-3:ipRangeFT:ipHCap
CurScore0-4:ipRangeFT:ipHCap
CurScore0-5:ipRangeFT:ipHCap
CurScore1-0:ipRangeFT:ipHCap
CurScore1-1:ipRangeFT:ipHCap
CurScore1-2:ipRangeFT:ipHCap
CurScore1-3:ipRangeFT:ipHCap
CurScore1-4:ipRangeFT:ipHCap
CurScore2-0:ipRangeFT:ipHCap
CurScore2-1:ipRangeFT:ipHCap
CurScore2-2:ipRangeFT:ipHCap
CurScore2-3:ipRangeFT:ipHCap
CurScore2-4:ipRangeFT:ipHCap
CurScore3-0:ipRangeFT:ipHCap
CurScore3-1:ipRangeFT:ipHCap
CurScore3-2:ipRangeFT:ipHCap
CurScore3-3:ipRangeFT:ipHCap
CurScore3-4:ipRangeFT:ipHCap
CurScore4-0:ipRangeFT:ipHCap
CurScore4-1:ipRangeFT:ipHCap
CurScore4-2:ipRangeFT:ipHCap
CurScore4-3:ipRangeFT:ipHCap
CurScore5-0:ipRangeFT:ipHCap
CurScore5-1:ipRangeFT:ipHCap
CurScore5-2:ipRangeFT:ipHCap
CurScore5-3:ipRangeFT:ipHCap
CurScoreNo:ipRangeFT:ipHCap
CurScore0-0:ipRangeHT:ipHCap 2.816
(2.827)
CurScore0-1:ipRangeHT:ipHCap -3.920
(4.091)
CurScore0-2:ipRangeHT:ipHCap -0.546
(6.250)
CurScore0-3:ipRangeHT:ipHCap -15.236
(36.431)
CurScore0-4:ipRangeHT:ipHCap
CurScore0-5:ipRangeHT:ipHCap
CurScore1-0:ipRangeHT:ipHCap -10.564***
(3.366)
CurScore1-1:ipRangeHT:ipHCap 12.865**
(5.736)
CurScore1-2:ipRangeHT:ipHCap -11.472
(10.620)
CurScore1-3:ipRangeHT:ipHCap -10.726
(12.180)
CurScore1-4:ipRangeHT:ipHCap
CurScore2-0:ipRangeHT:ipHCap 4.470
(3.123)
CurScore2-1:ipRangeHT:ipHCap 6.606
(8.595)
CurScore2-2:ipRangeHT:ipHCap -22.282
(14.411)
CurScore2-3:ipRangeHT:ipHCap -12.744
(35.127)
CurScore2-4:ipRangeHT:ipHCap
CurScore3-0:ipRangeHT:ipHCap 11.557*
(6.848)
CurScore3-1:ipRangeHT:ipHCap 9.641
(11.833)
CurScore3-2:ipRangeHT:ipHCap
CurScore3-3:ipRangeHT:ipHCap 12.354
(21.897)
CurScore3-4:ipRangeHT:ipHCap
CurScore4-0:ipRangeHT:ipHCap 1.289
(6.452)
CurScore4-1:ipRangeHT:ipHCap
CurScore4-2:ipRangeHT:ipHCap
CurScore4-3:ipRangeHT:ipHCap
CurScore5-0:ipRangeHT:ipHCap
CurScore5-1:ipRangeHT:ipHCap
CurScore5-2:ipRangeHT:ipHCap
CurScore5-3:ipRangeHT:ipHCap
CurScoreNo:ipRangeHT:ipHCap
CurScore0-0:ipRangeNo:ipHCap
CurScore0-1:ipRangeNo:ipHCap
CurScore0-2:ipRangeNo:ipHCap
CurScore0-3:ipRangeNo:ipHCap
CurScore0-4:ipRangeNo:ipHCap
CurScore0-5:ipRangeNo:ipHCap
CurScore1-0:ipRangeNo:ipHCap
CurScore1-1:ipRangeNo:ipHCap
CurScore1-2:ipRangeNo:ipHCap
CurScore1-3:ipRangeNo:ipHCap
CurScore1-4:ipRangeNo:ipHCap
CurScore2-0:ipRangeNo:ipHCap
CurScore2-1:ipRangeNo:ipHCap
CurScore2-2:ipRangeNo:ipHCap
CurScore2-3:ipRangeNo:ipHCap
CurScore2-4:ipRangeNo:ipHCap
CurScore3-0:ipRangeNo:ipHCap
CurScore3-1:ipRangeNo:ipHCap
CurScore3-2:ipRangeNo:ipHCap
CurScore3-3:ipRangeNo:ipHCap
CurScore3-4:ipRangeNo:ipHCap
CurScore4-0:ipRangeNo:ipHCap
CurScore4-1:ipRangeNo:ipHCap
CurScore4-2:ipRangeNo:ipHCap
CurScore4-3:ipRangeNo:ipHCap
CurScore5-0:ipRangeNo:ipHCap
CurScore5-1:ipRangeNo:ipHCap
CurScore5-2:ipRangeNo:ipHCap
CurScore5-3:ipRangeNo:ipHCap
CurScoreNo:ipRangeNo:ipHCap
Constant 48.725*** 0.687* 0.083 0.016 1.575* -0.200 1.446 -0.345 1.541* 0.172 71.966*** 0.079 0.102
(0.467) (0.386) (1.273) (1.303) (0.900) (0.363) (0.926) (0.554) (0.901) (0.956) (2.226) (1.052) (1.054)
Observations 48,640 48,640 48,640 48,640 48,640 35,304 48,640 35,304 48,640 35,304 48,640 35,304 35,304
R2 0.004 0.520 0.520 0.520 0.520 0.522 0.520 0.523 0.521 0.524 0.007 0.523 0.527
Adjusted R2 0.004 0.520 0.520 0.520 0.520 0.522 0.520 0.523 0.520 0.523 0.007 0.523 0.523
Residual Std. Error 80.747 (df = 48638) 56.076 (df = 48637) 56.076 (df = 48637) 56.076 (df = 48636) 56.069 (df = 48617) 54.057 (df = 35301) 56.069 (df = 48616) 54.050 (df = 35272) 56.065 (df = 48589) 54.033 (df = 35252) 80.654 (df = 48636) 54.038 (df = 35259) 54.026 (df = 34978)
F Statistic 215.124*** (df = 1; 48638) 26,329.510*** (df = 2; 48637) 26,329.750*** (df = 2; 48637) 17,552.850*** (df = 3; 48636) 2,395.595*** (df = 22; 48617) 19,309.660*** (df = 2; 35301) 2,291.423*** (df = 23; 48616) 1,247.355*** (df = 31; 35272) 1,054.940*** (df = 50; 48589) 759.494*** (df = 51; 35252) 109.988*** (df = 3; 48636) 879.822*** (df = 44; 35259) 120.082*** (df = 325; 34978)
Note: p<0.1; p<0.05; p<0.01

table 4.1.5 : Summary of linear models.

Statistic N Mean St. Dev. Min Max
Res.Df 5 48,633.000 8.972 48,617 48,638
RSS 5 185,755,154.000 73,436,276.000 152,839,454.000 317,121,936.000
Df 4 5.250 9.179 0 19
Sum of Sq 4 41,070,621.000 82,075,107.000 186.756 164,183,261.000
F 3 17,409.030 30,151.840 0.059 52,225.370
Pr(> F) 3 0.282 0.456 0.000 0.807
Statistic N Mean St. Dev. Min Max
Df 3 11,767.670 20,380.470 1 35,301
Sum Sq 3 72,001,537.000 62,542,706.000 723.720 112,849,861.000
Mean Sq 3 37,617,836.000 65,152,845.000 723.720 112,849,861.000
F value 2 19,309.660 27,307.630 0.248 38,619.070
Pr(> F) 2 0.309 0.438 0.000 0.619
Statistic N Mean St. Dev. Min Max
Df 4 12,159.750 24,304.170 1 48,616
Sum Sq 4 79,631,138.000 92,039,366.000 150.809 165,585,726.000
Mean Sq 4 41,398,449.000 82,791,518.000 150.809 165,585,726.000
F value 3 17,557.450 30,409.040 0.048 52,670.780
Pr(> F) 3 0.296 0.461 0.000 0.827
Statistic N Mean St. Dev. Min Max
Df 4 8,825.750 17,630.840 1 35,272
Sum Sq 4 54,001,153.000 62,418,544.000 1,380.011 112,849,861.000
Mean Sq 4 28,214,502.000 56,423,572.000 1,380.011 112,849,861.000
F value 3 12,877.050 22,302.160 0.472 38,629.360
Pr(> F) 3 0.203 0.257 0.000 0.492
Statistic N Mean St. Dev. Min Max
Df 4 12,159.750 24,286.170 1 48,589
Sum Sq 4 79,631,138.000 91,977,983.000 93,496.640 165,585,726.000
Mean Sq 4 41,399,403.000 82,790,882.000 3,143.251 165,585,726.000
F value 3 17,560.850 30,413.880 1.293 52,679.770
Pr(> F) 3 0.069 0.067 0.000 0.134
Statistic N Mean St. Dev. Min Max
Df 5 7,060.600 15,759.480 1 35,252
Sum Sq 5 43,200,922.000 59,152,060.000 1,550.930 112,849,861.000
Mean Sq 5 22,572,861.000 50,466,377.000 1,550.930 112,849,861.000
F value 4 9,664.360 19,326.090 0.531 38,653.490
Pr(> F) 4 0.147 0.220 0.000 0.466
Statistic N Mean St. Dev. Min Max
Df 4 12,159.750 24,317.500 1 48,636
Sum Sq 4 79,631,138.000 157,832,086.000 291,708.900 316,378,125.000
Mean Sq 4 538,232.900 605,002.700 6,505.019 1,402,616.000
F value 3 109.988 92.307 44.844 215.621
Pr(> F) 3 0.000 0.000 0 0
Statistic N Mean St. Dev. Min Max
Df 5 7,060.600 15,763.390 1 35,259
Sum Sq 5 43,200,922.000 59,170,043.000 723.720 112,849,861.000
Mean Sq 5 22,572,544.000 50,466,554.000 723.720 112,849,861.000
F value 4 9,662.259 19,322.250 0.248 38,645.630
Pr(> F) 4 0.278 0.325 0.000 0.619
Statistic N Mean St. Dev. Min Max
Df 6 5,883.833 14,253.560 1 34,978
Sum Sq 6 36,000,768.000 55,466,442.000 1,550.930 112,849,861.000
Mean Sq 6 18,811,219.000 46,069,338.000 1,550.930 112,849,861.000
F value 5 7,733.608 17,290.090 0.531 38,663.060
Pr(> F) 5 0.187 0.210 0.000 0.466

table 4.1.6 : Anova of linear models.

Based on table 2.2.1 we know about the net bookies probabilities and EM probabilities, here I simply apply linear regression model4 You can learn from Linear Regression in R (R Tutorial 5.1 to 5.11). You can also refer to Getting Started with Mixed Effect Models in R, A very basic tutorial for performing linear mixed effects analyses and Fitting Linear Mixed-Effects Models using lme4. Otherwise you can read Linear Models with R and somemore details about regression models via Extending the Linear Model with R : Generalized Linear, Mixed Effects and Nonparametric Regression Models. and also anova to compare among the models.

shinyapp 4.2.1 : Comparison of the vigorish between AH and Fixed-Odds. Source from 1x2 to Combo AH version 1.1 by William Chen (2006)

Here I simply attached with a Fixed Odds to Asian Handicap’s calculator which refer to my ex-colleague William Chen’s5 My ex-colleague and best friend in sportsbook industry which known since join sportsbook industry year 2005 —— Telebiz and later Caspo Inc. spreadsheet version 1.1 in year 2006. You can simply input the home win, draw, away win (in decimal format) as well as the overround.6 Kindly refer to my previous research to know the vigorish / overround.

shinyapp 4.2.2 : Convertion between AH and Fixed-Odds.

Section : reverse modelling to get the EMProb prior to calculate the coefficient of the staking model. Otherwise might rearrange the order of applied Poison model here by refer to international competitions.

Galema, Plantinga and Scholtens (2008)7 You are feel free to refer to [Reference for industry knowdelege and academic research portion for the paper] for further details

reminder (temporary noted for further):

draft : 
  - http://www.moneychimp.com/articles/risk/regression.htm
  - read *Galema, Plantinga and Scholtens (2008)* https://englianhu.files.wordpress.com/2016/06/the-stocks-at-stake-return-and-risk-in-socially-responsible-investment.pdf
  - reverse engineering on staking-profit linear regression model to get/retrieve EMProb value since now only get the coefficients figire of EMProb. Although incompleted soccer teams... 2ndly, reversed poison model from EMProb might is not workable on one-sided competition, need to refer to some international competition as references for incompleted dataset.

John Fingleton & Patrick Waldron (1999)8 You are feel free to refer to [Reference for industry knowdelege and academic research portion for the paper] for further details apply Shin’s model and finally conclude suggests that bookmakers in Ireland are infinitely risk-averse and balance their books. The authors cannot distinguish between inside information and operating costs, merely concluding that combined they account for up to 3.7% of turnover. They compare different versions of our model, using data from races in Ireland in 1993. The authors’ empirical results can be summarised as follows:

  • They reject the hypothesis that bookmakers behave in a riskneutral manner;
  • They cannot reject the hypothesis that they are infinitely riskaverse;
  • They estimate gross margins to be up to 4 per cent of total oncourse turnover; and
  • They estimate that 3.1 to 3.7% (by value) of all bets are placed by punters with inside information.

Here I try to test our data if there has any insider information.

4.3 Kelly Ⓜodel

From the papers Niko Marttinen 20019 Kindly refer to 1th paper in 7.4 References and Jeffrey Alan Logan Snyder 201310 Kindly refer to 2nd paper in 7.4 References both applying Full-Kelly,Half-Kelly and also Quarter-Kelly models which similar with my previous Kelly-Criterion model ®γσ, Eng Lian Hu 201411 Kindly refer to 4th paper in 7.4 References but enhanced.

To achieve the level of profitable betting, one must develop a correct money management procedure. The aim for a punter is to maximize the winnings and minimize the losses. If the punter is capable of predicting accurate probabilities for each match, the Edward O. Thorp 200612 Kindly refer to 6th paper in 7.4 References has proven to work effectively in betting. It was named after an American economist John Kelly (1956) and originally designed for information transmission. The Kelly criterion is described below:

\[S=(\rho*\sigma-1)/(\sigma-1)\] equation-4.3.1

Where S = the stake expressed as a fraction of one’s total bankroll, \(\rho\) = probability of an event to take place, \(\sigma\) = odds for an event offered by the bookmaker. Three important properties, mentioned by Hausch and Ziemba (1994) (Efficiency of Racetrack Betting Markets (2008Edition)), arise when using this criterion to determine a proper stake for each bet:

  • It maximizes the asymptotic growth rate of capital
  • Asymptotically, it minimizes the expected time to reach a specified goal
  • It outperforms in the long run any other essentially different strategy almost surely

The criterion is known to economists and financial theorists by names such as the geometric mean maximizing portfolio strategy, the growth-optimal strategy, the capital growth criterion, etc. We will now show that Kelly betting will maximize the expected log utility for sports-book betting.

[1] 23.71528

\[K = \frac{(B + 1)p - 1} {B}\] equation 4.3.1

\[G: = \mathop {\lim }\limits_{N \to \infty } \frac{1/N}{\log}\left( {\frac{{{BR_N}}}{{{BR_0}}}} \right)\] equation 4.3.2

\[BR_N = (1 + K)^W(1 - K)^L BR_0\] equation 4.3.3

Kelly K-value 凯利模式资金管理

## Bootstrapping to get the optimal value
#'@ llply(rEMProbB)

table 4.3.2

In order to get the optimal value, I apply the bootrapping and resampling method.

\[L(\rho) = \prod_{i=1}^{n} (x_{i}|\rho)\] equation 4.3.4

Now we look at abpve function from a different perspective by considering the observed values \(x1, x2, …, xn\) to be fixed parameters of this function, whereas \(\rho\) will be the function’s variable and allowed to vary freely; this function will be called the likelihood.

4.4 Poisson Ⓜodel

Here we introduce the Dixon & Coles 1996 Poisson model and its codes. You are freely learning from below links if interest.

table 4.4.1 : Filtered multiple bets placed on same matches.

Due to the soccer matches randomly getting from different leagues, and also not Bernoulli win-lose result but half win-lose etc as we see from above. Besides, there were mixed Pre-Games and also In-Play soccer matches and I filter-up the sample data to be 20009 x 45. I don’t pretend to know the correct answer or the model from firm A. However I take a sample presentation Robert Johnson (2011)13 Kindly refer to 23th paper in 7.4 References from one of consultancy firm which is Dixon-Coles model and omitted the scoring process section.

Here I cannot reverse computing from barely \(\rho_i^{EM}\) without know the \(\lambda_{ij}\) and \(\gamma\) values. Therefore I try to using both Home and Away Scores to simulate and test to get the maximum likelihood \(\rho_i^{EM}\).

\[X_{ij} = pois(\gamma \alpha_{ij} \beta_{ij} ); Y_{ij} = pois(\alpha_{ij} \beta_{ij})\] equation 4.4.1

sample…

In order to minimzie the risk, I tried to validate the odds price range invested by firm A.14 As I used to work in AS3388 which always take bets from Starlizard where they only placed bets within the odds price range from 0.70 ~ -0.70. They are not placed bets on all odds price in same edge. The sportbook consulatancy firms will not place same amount of stakes on same edge, lets take example as below :-

  • \(Odds_{em}\) = 0.40 while \(Odds_{BK}\) = 0.50, The edge to firm will be 0.5 ÷ 0.4 = 1.25
  • \(Odds_{em}\) = 0.64 while \(Odds_{BK}\) = 0.80, The edge to firm will be 0.8 ÷ 0.64 = 1.25

We know above edge is same but due to the probability of occurance an event/goal at 0.4 is smaller than 0.64. Here I try to bootstrap/resampling the scores of matches of the dataset and apply maximum likelihood on the poisson model to test the Kelly model and get the mean/likelihood value. Boostrapping the scores and staking model will be falling in the following sections 4.5 Staking Ⓜodel and Ⓜoney Management and 4.6 Expectation Ⓜaximization and Staking Simulation.

4.5 Staking Ⓜodel and Ⓜoney Management

Martin Spann and Bernd Skiera (2009)15 Kindly refer to 19th paper in 7.4 References applied a basic probability sets on the draw games and also the portion of win and loss. The author simply measured the portion of the draw result with win/loss to get the edge to place a bet. However it made a loss on Italian operator Oddset due to the 25% high vigorish but profitable in 12%. Secondly, the bets placed on fixed odds but not Asian Handicap and also a fixed amount $100.

sample… Geometric Mean

Parimutuel Betting

4.6 Expectation Ⓜaximization and Staking Simulation

sample…

5. Result

5.1 Comparison of the Results

Chapter 4.2 Comparison of Different Feature Sets and Betting Strategies in

Dixon&Pope2003 apply linear model to compare the efficiency of the odds prices offer by first three largest Firm A, B and C in UK.

5.2 Market Basket

Here I apply the arules and arulesViz packages to analyse the market basket of the bets.

6. Conclusion

6.1 Conclusion

Due to the data-sets I collected just one among all agents among couple sports-bookmakers 4lowin. Here I cannot determine if the sample data among the population…

JA: What skills and academic training (example: college courses) are valuable to sports statisticians? KW: I would say there are three sets of skills you need to be a successful sports statistician: - Quantitative skills - the statistical and mathematical techniques you’ll use to make sense of the data. Most kinds of coursework you’d find in an applied statistics program will be helpful. Regression methods, hypothesis testing, confidence intervals, inference, probability, ANOVA, multivariate analysis, linear and logistic models, clustering, time series, and data mining/machine learning would all be applicable. I’d include in this category designing charts, graphs, and other data visualizations to help present and communicate results. - Technical skills - learning one or more statistical software systems such as R/S-PLUS, SAS, SPSS, Stata, Matlab, etc. will give you the tools to apply quantitative skills in practice. Beyond that, the more self-reliant you are at extracting and manipulating your data directly, the more quickly you can explore your data and test ideas. So being adept with the technology you’re likely to encounter will help tremendously. Most of the information you’d be dealing with in sports statistics would be in a database, so learning SQL or another query language is important. In addition, mastering advanced spreadsheet skills such as pivot tables, macros, scripting, and chart customization would be useful. - Domain knowledge - truly understanding the sport you want to analyze professionally is critical to being successful. Knowing the rules of the game; studying how front offices operate; finding out how players are recruited, developed, and evaluated; and even just learning the jargon used within the industry will help you integrate into the organization. You’ll come to understand what problems are important to the GM and other decisionmakers, as well as what information is available, how it’s collected, what it means, and what its limitations are. Also, I recommend keeping up with the discussions in your sport’s analytic community so you know about the latest developments and what’s considered the state of the art in the public sphere. One of the great things about being a sports statistician is getting to follow your favorite websites and blogs as a legitimate part of your job!

source : Preparing for a Career as a Sports Statistician: Two Interviews with People in the Field

… … …

6.2 Future Works

I will be apply Shiny to write a dynamic website to utilise the function as web based apps. You are welcome to refer SHOW ME SHINY.

I will also write as a package to easier load and log.

7. Appendices

7.1 Documenting File Creation

It’s useful to record some information about how your file was created.

[1] “2016-08-24 00:01:34 JST” setting value
version R version 3.3.1 (2016-06-21) system x86_64, mingw32
ui RTerm
language (EN)
collate English_United States.1252
tz Asia/Tokyo
date 2016-08-24
sysname release version nodename “Windows” “10 x64” “build 10586” “RSTUDIO-SCIBROK” machine login user effective_user “x86-64” “scibr” “scibr” “scibr”

7.2 Versions’ Log

  • File pre-release version: 0.9.0
    • file created
    • Applied ggplot2, ggthemes, directlabels packages for ploting. For example, the graphs applied in Section 2. Data.
  • File pre-release version: 0.9.1
    • Added Natural Language Analysis which is research for teams’ name filtering purpose.
    • Changed from knitr::kable to use datatble from DT::datatable to make the tables be dynamic.
    • Changed from ggplot2 relevant packages to googleVis package to make graph dynamic.
    • Completed chapter 3. Summarise the Staking Model.
  • File pre-release version: 0.9.2 - “2016-02-20 09:41:49 JST”
  • File pre-release version: 0.9.3 - “2016-02-05 05:24:35 EST”
    • Modified DT::datatable to make the documents can be save as xls/csv
    • Added log file for version upgraded
  • File pre-release version: 0.9.3.1 - 2016-06-22 13:36:33 JST
    • Reviewed previous version, DT::datatable updated new version replaced Button extension from TableTools, removed sparkline and htmlwidget
    • Applied linear regression to test the efficiency of staking model by consultancy firm A

7.3 Speech and Blooper

Firstly I do appreciate those who shade me a light on my research. Meanwhile I do happy and learn from the research.

There are quite some errors when I knit HTML:

  • let say always stuck (which is not response and consider as completed) at 29%. I tried couple times while sometimes prompt me different errors (upgrade Droplet to larger RAM memory space doesn’t helps) and eventually apply rm() and gc() to remove the object after use and also clear the memory space.

  • Need to reload the package suppressAll(library('networkD3')) which in chunk decission-tree-A prior to apply function simpleNetwork while I load it in chunk libs at the beginning of the section 1. Otherwise cannot found that particlar function.

  • The rCharts::rPlot() works fine if run in chunk, but error when knit the rmarkdown file. Raised an issue : Error : rCharts::rPlot() in rmarkdown file.

  • xtable always shows LaTeX output but not table. Raised a question in COS : 求助！knitr Rmd pdf 中文编译 2016年8月19日 下午9:56 7 楼.Here I try other packages like textreg and stargazer.

7.4 References

Reference for industry knowdelege and academic research portion for the paper.

  1. Creating a Profitable Betting Strategy for Football by Using Statistical Modelling by Niko Marttinen (2006)
  2. What Actually Wins Soccer Matches: Prediction of the 2011-2012 Premier League for Fun and Profit by Jeffrey Alan Logan Snyder (2013)
  3. Odds Modelling and Testing Inefficiency of Sports Bookmakers : Rmodel by ®γσ, Eng Lian Hu (2016)
  4. Apply Kelly-Criterion on English Soccer 2011/12 to 2012/13 by ®γσ, Eng Lian Hu (2014)
  5. The Betting Machine by Martin Belgau Ellefsrød (2013)
  6. The Kelly Criterion in Blackjack Sports Betting, and the Stock Market by Edward Thorp (2016)
  7. Statistical Methodology for Profitable Sports Gambling by Fabián Enrique Moya (2012)
  8. How to apply the Kelly criterion when expected return may be negative? by user1443 (2011)
  9. Money Management Using The Kelly Criterion by Justin Kuepper
  10. Optimal Exchange Betting Strategy For WIN-DRAW-LOSS Markets by Darren O’Shaughnessy (2012)
  11. Kelly criterion with more than two outcomes by David Speyer (2014)
  12. 凯利模式资金管理 by Chung-Han Hsieh (2015)
  13. Optimal Determination of Bookmakers’ Betting Odds: Theory and Tests by John Fingleton & Patrick Waldron (1999)
  14. Optimal Pricing in the Online Betting Market by Maurizio Montone (2015)
  15. Why are Gambling Markets Organised so Differently from Financial Markets? by Steven Levitt (2004)
  16. Forecasting Accuracy and Line Changes in the NFL and College Football Betting Markets by Steven Xu (2013)
  17. The Forecast Ability of the Dispersion of Bookmaker Odds by Kwinten Derave (2013-2014)
  18. The Stocks at Stake: Return and Risk in Socially Responsible Investment by Galema, Plantinga and Scholtens (2008)
  19. A Comparison of the Forecast Accuracy of Prediction Markets, Betting Odds and Tipsters by Martin Spann and Bernd Skiera (2009)
  20. Efficiency of the Market for Racetrack Betting by Donald Hausch, William Ziemba and Mark Rubinstein (1981)
  21. Betting Market Efficient at Premiere Racetracks by Marshall Gramm (2011)
  22. Late Money and Betting Market Efficiency: Evidence from Australia by Marshall Gramm, Nicholas McKinney and Randall Parker (2012)
  23. An introduction to football modelling at Smartodds by Robert Johnson (2011)
  24. The Value of Statistical Forecasts in the UK Association Football Betting Market by Dixon and Pope (2003)
  25. Modelling Association Football Scores and Inefficiencies in the Football Betting Market by Dixon & Coles 1996

Author image syui

Financial Evaluation and Strategy: Corporate Finance : Module 4

Financial Evaluation and Strategy: Corporate Finance : Module 4

Improving Business Finances and Operations Specialization by University of Illinois at Urbana-Champaign

®γσ, Eng Lian Hu 白戸則道®

2016-08-02

1. Introduction

1.1 Overview

Instructions

The purpose of this assignment is to give you the opportunity to apply the concepts you have learned in this module and to discuss some of the key ideas of the module in your own words. Follow the instructions provided and respond to each question. This a required activity for this module. The activity is peer reviewed, so after you submit your responses, you will review submissions by fellow learners in the course.

1.2 Instructions

There are multiple steps to this assignment.

First, you will submit your answers to each questions based on the information in the Assignment Details section. Enter your answers directly in the spaces provided in the My submission tab. You may save a draft of your work as you go, and you can come back later to continue working on your draft. When you are finished working, click the Preview button, verify your identity, and then Submit the assignment. Please answer each question fully and concisely.

Then, you will evaluate the submissions of at least THREE of your peers based on the instructions provided. You may begin giving feedback to other students as soon as you submit your assignment, click the Review peers tab to begin. Feel free to provide additional reviews beyond the three required!

Assignment 4 is described in Video Lesson 4-14, you should watch this video before doing the assignment.

The discussion of the assignment solution is provided in Video Lesson 4-15. Do the assignment on your own first, before viewing the assignment discussion video! Please view the assignment discussion video before completing the review of your peers.

1.3 Review criteria

For Assignment #4, you will be responsible for evaluating the submissions of THREE of your peers. Before evaluating, please see the video I prepared with my discussion of the answers to Assignment #4.

Assignment #4 is worth 100 points total. Points are only given for correct/reasonable answers in the manner specified below, incorrect/unreasonable answers get zero points. Points should be allocated as follows:

1.3.1 Question 1

1.3.1.1 Question 1-a

  • 20 points for a complete answer that is correct. To get 10 points the student should set up the cash flows correctly, and calculate the correct NPV of the synergies
  • 15 points for a good answer that has calculation mistakes. For example if the student sets up the right decision tree but makes a calculation mistake to get the NPV
  • 10 points for an incomplete answer

1.3.1.2 Question 1-b

  • 10 points for a reasonable answer that is consistent with the analysis in part a)
  • 5 points for an incomplete answer

1.3.1.3 Question 1-c

  • 10 points for a reasonable answer that is based in the mini-case data and the arguments in the lectures
  • 5 points for an incomplete answer

1.3.2 Question 2

  • 10 points for a reasonable answer that is based on the arguments that we discussed in the lectures
  • 5 points for an incomplete answer

1.3.3 Question 3

  • 10 points for a reasonable answer that is based on the arguments that we discussed in the lectures
  • 5 points for an incomplete answer

1.3.4 Question 4

  • 20 points for a reasonable answer that correctly discusses both whether the Beta is 1.1, and suggests a reasonable way of estimating the Beta
  • 10 points for an incomplete answer, for example if the suggestion to calculate Beta does not make sense

1.3.5 Question 5

  • 10 points for the correct calculation of the WACC
  • 5 points for an incomplete answer

1.3.6 Question 6

  • 10 points for a reasonable answer that is consistent with the analysis in question 5
  • 5 points for an incomplete answer or an answer that is too long (longer than 1 paragraph)

1.3.7 Question 7

  • 10 points for the correct calculation of the EVA
  • 5 points for an incomplete answer

1.3.8 Question 8

  • 10 points for a reasonable answer that is consistent with the analysis in question 7
  • 5 points for an incomplete answer or an answer that is too long (longer than 1 paragraph)

Recommendations for Fair Peer Review:

  • For questions that require calculations only, the score should be based on whether or not the answer provided is correct.
  • For subjective questions, the score should not be based on whether or not you agree with the answer, rather on whether the answer is complete and well-supported.
  • Both content and organization are important components of a response. Good writing is confident and clearly focused with relevant details to enrich the content. Good writing also follows instructions, such as word limits, and offers requested information.
  • A clear and concise answer is preferable to a long response that lacks coherence.Focus should be on content; try not to unduly penalize responses for spelling or grammar.

1.4 Reminders

1.4.1 Using the Forums

Your fellow students are a great resource, and we encourage you to sharpen your ideas against them in the forums. You can post your arguments in the Module 1 Forum and receive feedback before submitting this assignment. Additionally, make sure to pay attention to posts from the instructors, which are intended to spur conversation on topics related to the week’s theme.

1.4.2 Honor Code

Please remember that you have agreed to the Honor Code, and your submission should be entirely yours. Our definition of plagiarism follows from standard literature: passing off someone else’s work as your own, whether from your peers or Wikipedia. If you need to quote material, remember to cite your source, for example: “But, as expressed by Spinoza, all things excellent are as difficult as they are rare (Baruch Spinoza,”Ethica" source: thinkexist.com)."

2. Case Study

Important Information

It is especially important to submit this assignment before the deadline, August 7, 11:59 PM PDT, because it must be graded by others. If you submit late, there may not be enough classmates around to review your work. This makes it difficult - and in some cases, impossible - to produce a grade. Submit on time to avoid these risks.

2.1 Question 1

On September 4th, 2009 (Friday), Cadbury’s shares closed trading at 5.71 pounds a share in London. The firm had 1.37 billion shares outstanding at that point. At current exchange rates, the market valuation of the firm in dollars was 12.83 billion dollars. On the weekend of September 4th to 7th (Monday was a holiday), Kraft announced a bid for all of Cadbury’s shares. The bid, which included both cash and shares, valued Cadbury at 7.45 pounds a share. The market responded enthusiastically to the bid, increasing Cadbury’s share price to 7.91 pounds at closing on September 8th, the first day of trading following the merger announcement.

Kraft’s management was criticized for trying to buy Cadbury on the cheap. Kraft had closed trading on Sep 4th at 28.1 dollars a share, which was a full 9% below its 2001 IPO price. This lackluster stock price performance also suggested that the firm had struggled to create value from its string of acquisitions. The market was not kind to Kraft, whose shares traded at 26.45 dollars at close on Sep 8th. The firm had 1.48 billion shares outstanding.

Kraft’s management justified the merger by arguing that it would produce 625 million dollars of annual cost savings, from operations, general and administrative expenses and marketing. These annual cost savings are expected to begin a year from now, and grow at 2% a year. Even after accounting for an after-tax integration cost of 1.2 billion, and taxes of 35%, these annual cost savings could easily justify the premium offered to Cadbury, according to Kraft’s managers (even without taking any potential revenue enhancements into account). Assume that the integration cost of 1.2 billion happens right when the merger is completed (one year before the annual cost savings begin).

The food industry’s Beta is on the low side (close to 0.6), so Kraft’s cost of capital (its WACC) is not very high (around 8%).

2.1.1 Question 1-A

Question:

Compute the value of the synergy as estimated by the management.

Answer:

Investors in a company that are aiming to take over another one must determine whether the purchase will be beneficial to them. In order to do so, they must ask themselves how much the company being acquired is really worth.

Naturally, both sides of an M&A deal will have different ideas about the worth of a target company: its seller will tend to value the company at as high of a price as possible, while the buyer will try to get the lowest price that he can.

There are, however, many legitimate ways to value companies. The most common method is to look at comparable companies in an industry, but deal makers employ a variety of other methods and tools when assessing a target company. Here are just a few of them:

  1. Comparative Ratios - The following are two examples of the many comparative metrics on which acquiring companies may base their offers:
    • Price-Earnings Ratio (P/E Ratio) - With the use of this ratio, an acquiring company makes an offer that is a multiple of the earnings of the target company. Looking at the P/E for all the stocks within the same industry group will give the acquiring company good guidance for what the target’s P/E multiple should be.
    • Enterprise-Value-to-Sales Ratio (EV/Sales) - With this ratio, the acquiring company makes an offer as a multiple of the revenues, again, while being aware of the price-to-sales ratio of other companies in the industry.
  2. Replacement Cost - In a few cases, acquisitions are based on the cost of replacing the target company. For simplicity’s sake, suppose the value of a company is simply the sum of all its equipment and staffing costs. The acquiring company can literally order the target to sell at that price, or it will create a competitor for the same cost. Naturally, it takes a long time to assemble good management, acquire property and get the right equipment. This method of establishing a price certainly wouldn’t make much sense in a service industry where the key assets - people and ideas - are hard to value and develop.
  3. Discounted Cash Flow (DCF) - A key valuation tool in M&A, discounted cash flow analysis determines a company’s current value according to its estimated future cash flows. Forecasted free cash flows (net income + depreciation/amortization - capital expenditures - change in working capital) are discounted to a present value using the company’s weighted average costs of capital (WACC). Admittedly, DCF is tricky to get right, but few tools can rival this valuation method.

Synergy: The Premium for Potential Success

For the most part, acquiring companies nearly always pay a substantial premium on the stock market value of the companies they buy. The justification for doing so nearly always boils down to the notion of synergy; a merger benefits shareholders when a company’s post-merger share price increases by the value of potential synergy.

Let’s face it, it would be highly unlikely for rational owners to sell if they would benefit more by not selling. That means buyers will need to pay a premium if they hope to acquire the company, regardless of what pre-merger valuation tells them. For sellers, that premium represents their company’s future prospects. For buyers, the premium represents part of the post-merger synergy they expect can be achieved. The following equation offers a good way to think about synergy and how to determine whether a deal makes sense. The equation solves for the minimum required synergy:

\[\frac{premerge\ value\ of\ both\ companies + synergy}{post\ merged\ number\ of\ shares}-premerge\ stock\ price \cdots equation\ 2.1.1\]

Read more at Mergers and Acquisitions: Valuation Matters1 You can also refer to How to calculate synergies in M&A for further reference

table 2.1.1: Stock price statement of company Cadbury and Kraft in acquisation.

table 2.1.2: The synergy value of acquisation by Kraft.

  • \(NPV_{Synergies}\) of year 2009: 406.25M ÷ (8% - 2%) - 1,200M = $5570.83M2 Kindly refer to reference 4th paper inside 4.4 References to know the formula about NPV
  • After-Tax Cash flow of year 2011 : $406.25M x 102% growth rates = $414.38M

You can refer to Acquisition of Cadbury by Kraft Foods for more information.3 Here are some relevant articles about acquisation: The inside story of the Cadbury takeover and Kraft buys Cadbury for £11.9bn: a Q&A

2.1.2 Question 1-B

Question:

By refer to question 1, does the estimate of synergies in a) justify the premium that Kraft offered to Cadbury?

Answer:

  • By refer to table 2.1.1, we know the ratio of bid price by 4th sep 2016 price = ($7.45 - $5.71) ÷ $5.71 x 100% = 30.47%
  • By refer to table 2.1.1, we know the market value, then we calculate the premium paid = $12.83bil x 30.47% = $3.91bil
  • \(NPV_{Synergies} - Premium_{Paid}\) : $5.57bil - $3.91bil = $1.66bil.

2.1.3 Question 1-C

Question:

By refer to question 1, did the market agree with the management’s valuation of synergies? Discuss (2 paragraphs maximum)

Answer:

  - From the decreasing of counter Kraft's stock price from $28.1 to $26.45 (decreased ($28.1 - $26.45) ÷ $28.1 = 5.87%), we can know the acquisation dicision made by management dislike by market.
  - The paper loss on equity value is 1.48 bil shares x ($28.1 - $26.45) = $2.44bil.
  - The financial market reaction on the falling stock price of Kraft might due to overpay to acquire Cadbury.
  - Cadbury's stock price increased from valued $7.45 to $7.91 means Cadbury's shareholders have been made profit from the overpay.

What are ‘Outstanding Shares’

Outstanding shares refer to a company’s stock currently held by all its shareholders, including share blocks held by institutional investors and restricted shares owned by the company’s officers and insiders. Outstanding shares are shown on a company’s balance sheet under the heading “Capital Stock.” The number of outstanding shares is used in calculating key metrics such as a company’s market capitalization, as well as its earnings per share (EPS) and cash flow per share (CFPS).

A company’s number of outstanding shares is not static, but may fluctuate widely over time. Also known as “shares outstanding.”

Read more: Outstanding Shares Definition | Investopedia

2.2 Question 2

Question:

Discuss the following statement: “US companies have a lot of excess cash on their balance sheets. Thus, we expect merger activity to increase (because firms must find ways to use their cash). In addition, these mergers (which should be mostly funded with cash holdings) are expected to be value-enhancing for acquirers.” (1 paragraph)

Answer:

  - A rich company might hold a lot of cash.
    * It can give dividends to shareholders.
    * Conduct acquisation activity to expend the business.
    * Invest in R&D to invent new products.
    * Invest on property assets.
  - However, above activities others than payback dividends to shareholders might need to do throughly study and research prior to spend the money.

2.3 Question 3

Question:

A company with virtually no debt, stable cash flow, and moderate growth prospects has become the target for a private equity acquisition (LBO). The company’s CEO is concerned that an LBO may result in significant job losses, given the track record of this particular PE fund. Which advice would you give to the CEO? (1 paragraph)

Answer:

  - Normally, a private equity fund will looking for undervalued company for acquisation. They will restructure the company to create value and growth to make profit. Eventually will sell the company if there has other more profitable opportunity cost.
  - The CEO of company need to restucture the company, convince the shareholders, and also set a long term policy to growth the company. All action need to be taken before the company takeover by private equity fund which do preparation for bargain and dealing.
  - Since the company is undervalue, it means that the current CEO is a good leader which have a propective vision to growth the company in stable pace. Therefore the private equity fund might high probably keep employ who as CEO after acquisation.

What is the difference between a hedge fund and a private equity fund?

Although their investor profiles are often similar, there are significant differences between the aims and types of investments sought by hedge funds and private equity funds.

Both hedge funds and private equity funds appeal to high net worth individuals (many require minimum investments of $250,000 or more), traditionally are structured as limited partnerships and involve paying the managing partners basic management fees plus a percentage of profits.

Read more: What is the difference between a hedge fund and a private equity fund? | Investopedia

2.4 Question 4

Question:

Yahoo holds a large stake in Alibaba Group Holdings, a Chinese e-commerce company. The value of this stake has been estimated to be greater than 30 billion dollars. Yahoo’s market capitalization is approximately 35 billion dollars. According to Capital IQ, Yahoo’s Beta is 1.11. Would it be appropriate to use Yahoo’s Beta to compute the cost of capital for Yahoo? Why or why not? How would you estimate a WACC for Yahoo? (2 paragraphs)

Answer:

figure 2.4.1: The business of Jack Ma

figure 2.4.1: The business of Jack Ma

You can refer to Jack Ma: China’s Alibaba Wants to Acquire Yahoo for more details about the relationship between Yahoo and Alibaba.

equation 2.4.1: WACC.

equation 2.4.1: WACC.

What is ‘Weighted Average Cost Of Capital - WACC’

Weighted average cost of capital (WACC) is a calculation of a firm’s cost of capital in which each category of capital is proportionately weighted.

Read more: Weighted Average Cost Of Capital (WACC) Definition | Investopedia

equation 2.4.2: Beta and risk.

equation 2.4.2: Beta and risk.

  • We can know Yahoo occupied the portion of 39% shares of Alibaba from above diagram. (the diagram of figure 2.3.1 might not same period with the situation in the question since there has no any date given inside the question.)
  • \(Beta_{Yahoo} = 1.11\)
  • \(Market.Value_{Alibaba}\) = \(30 bil\)
  • \(Market.Value_{Yahoo} = \$35 bil\)
  • By refer to equation 2.4.1, the given information in question 2.3 is insufficient to calculate and get the answer.

2.5 Question 5

Question:

The following data refers to Coca Cola (NYSE: KO)

  • Beta = 0.5
  • Required return on debt (yield to maturity on a long term bond) = 3.5%
  • Tax rate = 25%
  • Estimate the cost of capital (WACC) for Coca Cola.

Answer:

equation 2.4.2: The required return on equity.

equation 2.4.2: The required return on equity.

  • By refer to equation 2.4.1, WACC = 3.5% x (1 - 25%) x (Total debt ÷ V) + rE x (E ÷ V)
  • By refer to equation 2.4.2 and equation 2.5.1, rE = 3% + 0.5 x 5% = 5.5%
  • Due to the question doesn’t provide the dataset or which financial year The Coca-Cola Co(NYSE:KO), therefore unable to know the value V ÷ D.

2.6 Question 6

Question:

How does Coca Cola’s WACC compare to Pepsico? Does this comparison make sense to you? (1 paragraph)

Answer:

  - Both companies are global recognizable public listed company in beverage industry. The WACC should be similar or no big difference.

2.7 Question 7

Question:

Now consider Coca Cola’s income statement and balance sheet, and compute EVA in 2014 as we did for Pepsico.

Answer:

What is ‘Economic Value Added - EVA’

Economic value added (EVA) is a measure of a company’s financial performance based on the residual wealth calculated by deducting its cost of capital from its operating profit, adjusted for taxes on a cash basis. EVA can also be referred to as economic profit, and it attempts to capture the true economic profit of a company. This measure was devised by Stern Stewart and Co…

Calculating EVA

The formula for calculating EVA is: Net Operating Profit After Taxes (NOPAT) - Invested Capital * Weighted Average Cost of Capital (WACC)

Read more: Economic Value Added (EVA) Definition | Investopedia

2.8 Question 8

Question:

How does Coca Cola’s EVA compare with Pepsico? Discuss. (1 paragraph)

Answer:

  - Economic profit = NOPAT – Cost of capital × Invested capital
  = PEP : $6,991 – 6.59% × $59,168 = $3091.83
  - KO : $0,000 – 0.00% × $00,000 = $0

  - Economic profit = NOPAT – Cost of capital × Invested capital
  - EVA Coca-Cola = $8,666 - 5% x $83,065 = $4,512
  - EVA Pepsico = $7,800 - 5% x 61,783 = $4,677

3. Conclusion

You are feel free to refer to below answer video provided by lecturer. However there are quite some data and formlura are not completed.

4. Appendices

4.1 Documenting File Creation

It’s useful to record some information about how your file was created.

[1] “2016-08-02 23:35:27 JST” setting value
version R version 3.3.1 (2016-06-21) system x86_64, mingw32
ui RTerm
language (EN)
collate English_United States.1252
tz Asia/Tokyo
date 2016-08-02
sysname release version nodename “Windows” “10 x64” “build 10586” “RSTUDIO-SCIBROK” machine login user effective_user “x86-64” “scibr” “scibr” “scibr”

4.2 Versions’ Log

4.3 Speech and Blooper

I do appreciate that University of Illinois at Urbana–Champaign provides the Improving Business Finances and Operations specialization via Coursera. I used to study Certified Accounting Technician (CAT) course at PAAC more more decade. Now I need to review the finance and accounting course prior to conduct my research Analyse the Finance and Stocks Price of Bookmakers.

There are few books below that I need to read for further understanding.

Initially, I can get the data and all the figure of PepsiCo, but when I try to get the data of Coca-cola, the figure suddenly mosaicsed and paid account required.

Author image syui

Managerial Accounting: Tools for Facilitating and Guiding Business Decisions : Module 4 Mini-Project

Managerial Accounting: Tools for Facilitating and Guiding Business Decisions : Module 4 Mini-Project

Improving Business Finances and Operations Specialization by University of Illinois at Urbana-Champaign

®γσ, Eng Lian Hu 白戸則道®

2016-08-08

1. Introduction

1.1 Instructions

1.1.1 Overview

There are multiple steps to this mini-project. First, you will submit your answers to the questions in Parts 1, 2, and 3 based on the information in the Assignment Details section. Enter your answers directly in the spaces provided in the My submission tab. Please answer each question fully and concisely, including the steps of your calculations and/or citations as needed (you may use the library guidelines to citations as a guide). Then, you will evaluate the submission of at least four of your peers based on the instructions provided.

1.1.2 How to Use Peer Review

  1. Submit your own assignment. Click the My submission tab to begin working on your own assignment. You can save drafts of your work as you go, and you can come back later to continue working on your draft. When you are finished working, click the Preview button, verify your identity, and then Submit the assignment

  2. Give feedback to your peers. You are required to give feedback to at least four peers to complete this assignment. You can begin giving feedback to other students as soon as you submit your assignment. Click the Review peers tab to get started. Feel free to provide additional reviews beyond the four required!

  3. Read feedback from your peers.Your peers will also begin reviewing your project as soon as you submit it. You will receive an email notification of each new review. Only you will be able to see the feedback you receive. If you find someone’s review helpful, click the This review is helpful button to thank the reviewer. Browse other projects. You can browse through all of the submitted assignments, even if you don’t plan to review each one. Click the like button if you think someone did a great job on their assignment.

1.1.3 Assignment Details

Choose an organizational setting and envision a strategic performance measurement system that would help facilitate and influence managers’ and employees’ actions and decisions related to pursuing organizational goals.

The following are potential settings on which to focus. Again, you only need to choose one setting.

  • Business school within a large, public university
  • Recently opened food stand owned by an entrepreneur chef
  • Sports team ownership group (sport of your choosing)
  • Large-scale manufacturer
  • Not-for-profit organization addressing poverty issues in a local community

Note: If none of the above scenarios are interesting to you, please feel free to identify and use one of your choosing.

Your Deliverable

  • Part 1: Clearly identify and describe your setting of interest.
  • Part 2: Briefly describe the overarching strategy of the organization, as well as the various perspectives (e.g., customer perspective, etc.) that the organization could adopt.
  • Part 3: Identify and describe no less than four organizational goals/objectives relevant to your setting. Be specific.
  • Part 4: Identify and describe at least two measures that correspond to each goal you identified in Part 3. Describe the measures in enough detail that would allow someone to implement and use the measure (i.e., how is the measure captured, what scale is used for the measure, etc.)
  • Part 5: Describe how you would provide incentives to managers and employees based on (at least) two of the measures you identified in Part 4.
  • Part 6: How might managers use subjective performance evaluation in this setting?

1.2 Review criteria

You will give a quantitative assessment of all parts of the submission. Then, you will provide qualitative feedback for the submission as a whole.

The following represents a guide for the quantitative assessment of Part 1-3:

  • 0 points: No answer, completely irrelevant answer, inadequate material, and/or evidence does not fit the argument.
  • 5 points: Insufficient answer, incomplete, lacks supporting evidence. An insufficientresponse is incomplete or incorrect. For calculations, the response fails to provide supporting calculations/steps.
  • 7 points: Passing, meets expectations. A passing response addresses/answers the question, but some of the answer is not thoroughly explained. For calculations, the supporting calculations/steps are not clear.
  • 9 points: Well above average, exceeds expectations An above average response addresses/answers the entire question and most of the answer is thoroughly explained. For calculations, most of the supporting calculations/steps are clear, but there are some minor deficiencies.
  • 10 points: Superior performance, excellent. An excellent response answers the entire question, and thoroughly explains the answer. For calculations, all supporting calculations/steps are clearly presented.

Recommendations for Fair Peer Review:

  • The score should not be based on whether or not you agree with the answer, rather on whether the answer is complete and well-supported. Both content and organization are important components of a response. Good writing is confident and clearly focused with relevant details to enrich the content. Good writing also follows instructions, such as word limits, and offers requested information.
  • A clear and concise answer is preferable to a long response that lacks coherence.
  • Focus should be on content; try not to unduly penalize responses for spelling or grammar.

1.3 Reminders

Using the Forums

Your fellow students are a great resource, and we encourage you to sharpen your ideas against them in the forums. You can post your arguments in the forums and receive feedback before submitting your assignment.

Honor Code

Please remember that you have agreed to the Honor Code, and your submission should be entirely yours. Our definition of plagiarism follows from standard literature: passing off someone else’s work as your own, whether from your peers or Wikipedia. If you need to quote material, remember to cite your source, for example: “But, as expressed by Spinoza, all things excellent are as difficult as they are rare (Baruch Spinoza,”Ethica" source: thinkexist.com)."

2. Case Study

2.1 Part 1

Question:

Using the information provided in the Assignment Details section of the Instructions tab, choose an organizational setting. Clearly identify and describe your setting of interest.

Answer:

I do choose Sports team ownership group (soccer sport) as my 4th assignment.

I have started refer to some references for my project Analyse the Finance and Stocks Price of Bookmakers which includes:

  • The economics of soccer sports.
  • The economics of soccer betting industry.
  • Analysis of the public listed sportsbook makers.
  • Analysis of Anonymous sportbookmakers’ product profit & loss.

My first job to join sportsbook industry in year 2005 is Betworks/AS3388. I heard from my senior SK (Lee Seow Kheong) told that the CTO (Chief Technology Officer) of Telebiz used to work for AS Roma as chief programmer to write the AS Roma’s website prior to join Telebiz and MG-SC Sdn Bhd. AS3388 is one of follower to Starlizard. I heard from my ex-colleague who work with SmartOdds who said Starlizard has venture business with AS3388 and has strong background with Italian Mafia compare to SmartOdds.

figure 2.1.1: Italian soccer club AS Roma and Captain Francesco Totti.

figure 2.1.1: Italian soccer club AS Roma and Captain Francesco Totti.

2.2 Part 2

Question:

Briefly describe the overarching strategy of the organization, as well as the various perspectives (e.g., customer perspective, etc.) that the organization could adopt.

Answer:

From Financial Evaluation and Strategy: Corporate Finance : Module 1 by ®yo, Eng Lian Hu 20161 Please refer to 5th reference paper in 4.4 References., we know a business group pursuit for profit.

table 2.2.1 : financial statement of AS Roma.

table 2.2.1 : financial statement of AS Roma.

You are feel free to browse over the financial statement of vaious soccer clubs via FOOTBALL ECONOMY.COM: A.S. Roma SpA | Associazione Sportiva Roma or latest news & updates from AS Roma official website.

From above table, we know that AS Roma used to make loss before year 2007/08. Then we try to refer to Stephen Morrow 20062 Kindly refer to 2nd reference paper in 4.4 References, the paper has states Italian Serie A clubs reported a loss (not only AS Roma, you might refer to every single Italian soccer clubs from the link from last paragraph) as below :-

  Over a number of years, many prominent Italian clubs had invested heavily in player purchases and related salaries. However, in the most recent years revenues had failed to grow at the same pace, such that at the end of season 2003/04, Serie A clubs reported a global operating loss of €948m (Paterson, 2004), with total debts of approximately €2.5bn (Deloitte & Touche, 2004).

Lets look at the Carmine Zoccali 20113 Kindly refer to 3rd paper in 4.4 References which has conduct a case study on the financial issues of Italian soccer clubs.

  • The paper observed on Italian football clubs, playing in Serie A, Serie B and Lega-Pro leagues, went out of business during the period 2006-2010.
  • In the observation period, 52 football clubs went out of business, and of these: 7 after relegation (the red ones in italics), 7 after promotion (the yellow ones in bold) and 2 after repechage (the green ones underlined).
  • The participation of each Italian club in its league depends on the correct functioning of a univariate model. This research highlights how, among the ratios adopted bythe Italian watchdog committee, only the ratio Equity to Total assets (E/TA)4 Kindly refer to graph 2.2.1. isable to completely split bankrupt from non-bankrupt football clubs. The othersratios (VP/DF and R/I) do not have the same ability because their mean valuesoverlap time after time. These ratios have no ability to predict firms’ failure anddecisions to raise or reduce their level do not give a significant variation in theability of predicting failure.
table 2.2.2 : Bankruptcy of Italian soccer clubs.

table 2.2.2 : Bankruptcy of Italian soccer clubs.

table 2.2.3 : Selected sample Italian soccer clubs.

What is the ‘Shareholder Equity Ratio’

The shareholder equity ratio determines how much shareholders would receive in the event of a company-wide liquidation. The ratio, expressed as a percentage, is calculated by dividing total shareholders’ equity by total assets of the firm, and it represents the amount of assets on which shareholders have a residual claim. The figures used to calculate the ratio are taken from the company balance sheet.

\[Shareholder\ Equity\ Ratio = \frac{Total\ Shareholder\ Equity}{Total Assets} \cdots equation\ 2.2.1\]

Read more: Shareholder Equity Ratio Definition | Investopedia

graph 2.2.1 : total shareholders equity / total assets.

graph 2.2.1 : total shareholders equity / total assets.

table 2.2.4 : The failure rate of VP ÷ DF.

table 2.2.4 : The failure rate of VP ÷ DF.

table 2.2.5 : The failure rate of VP ÷ DF after reducing the ratio RI over 1.40.

table 2.2.5 : The failure rate of VP ÷ DF after reducing the ratio RI over 1.40.

Stephen Morrow 20065 Kindly refer to 2nd reference paper in 4.4 References also states below points cause a deficit financial statement :

  • European EUFA licening system issue.
  • High wages and transfering fees for players.
  • High taxes for government.
  • Overvalued of the signed players.
  • Political business, for example the Italian prime minister is the shareholder of AC Milan.
graph 2.2.1 : Italian soccer clubs transfer fees

graph 2.2.1 : Italian soccer clubs transfer fees

  - Based on above statement and also data analysis, we can know the most of Italian clubs' (not only AS Roma) shareholders benefit has been has been abused by the management which might probably bought over-valued players.
  
  - Lets assume that the supporters are customers since they spend money to watch the competition in the stadium and also some clothes and gifts. They would expect the manager and the teams have quality and high productivity (high scores, high ranking, and acquite more awards etc.)
  
  - The shareholders expect the management conduct a profitable business and supporters expect the team has high quality. Therefore the team need to be more focus on the practice and the competition, the salary paid will be increased depends on the ability. Undervalued will be only temporary for the players and manager if they keep up practice to be stronger and eventually proof by the achievement.

2.3 Part 3

Question:

Identify and describe no less than four organizational goals/objectives relevant to your setting. Be specific.

Answer:

  - Always put the results, achievement as first priority since the high productivity is high quality of the team and also brilliant management. Players will be awarded both prize and salary paid based on performance. Same theory applied to with manager.
  
  - Always planted the idea of patriotism and honorific mindset to the clubs and also nations especially participate EUFA and other international matches. Proud as the team members and also the nations, both individual and team achievement are rewards and also spirit to supporters.
  
  - Set a target and goal to achieve, from history result AS Roma had below honors:-
  
    + Serie A : Winners (3): 1941–42, 1982–83, 2000–01
    + Coppa Italia : Winners (9): 1963–64, 1968–69, 1979–80, 1980–81, 1983–84, 1985–86, 1990–91, 2006–07, 2007–08
    + Supercoppa Italiana : Winners (2): 2001, 2007
    + Serie B : Winners (1): 1951–52
    + Inter-Cities Fairs Cup : Winners (1): 1960–61
    Source from https://en.wikipedia.org/wiki/A.S._Roma.
    
  - From above achievement, we can know AS Roma used to rank in Serie B few decades ago and slowly stronger and awards quite some times of winners in various national competitions.

2.4 Part 4

Question:

Identify and describe at least two measures that correspond to each goal you identified in Part 3. Describe the measures in enough detail that would allow someone to implement and use the measure (i.e., how is the measure captured, what scale is used for the measure, etc.)

Answer:

  - Provides efficient practice and training and players allocation base on whose strength.
  
  - Do upgrade the equipment, venue and scedule for training. For example, Alex Ferguson from Manchester United is a good manager who lead Man Utd to be one of the best clubs in the World. His organization skill and also planing skill are very good. Not only good management but also the high technology training material and equipment which fit for players. A physiotherapist who also keep track on the healthiness and fitness of the players for every single participated games and giving advice, cure and also medical assistant to the players.
  
  - An adequate training schedule with sufficient rest time to players to increase the efficiency. Physiotherapist always play an importance role to co-orperates with manager.
  
  - Manager need to give an appropriate reward and punishment to players. Stimulate players and also arrange players to play with appropriate role and position base on thier strengthen. Always observe and also discuss with players from both training and match competition to know the level and progress of the players to handle his position.
  
  - Sometimes the stress to players especially UEFA Championship. Need to provides an efficient rest and consultance to them.

2.5 Part 5

Question:

Describe how you would provide incentives to managers and employees based on (at least) two of the measures you identified in Part 4.

Answer:

 - Base on the performance, the incentives to manager and players will definitely increase if there has any achievement.
 
 - The awards not only phisically rewards to the team but also stimulate them to keep up fighting for the next season. Achievement might cause the spiritual effects to the team as well. Once a team keep up leading the league, the n the team will always represent the nation to participate the UEFA and proud to the nation but not only individual or the club. For example, AS Roma's result in season 2000/01.
 
 - A high productivity (high scoring, high wining rates and less loss goals) can lead to famous, and the income generates from the commercial advertisement and also shirts, gifts. Meanwhile the attendance and broadcasting will also increase. Shareholders of the football group will eventually get high return from the investment.

2.6 Part 6

Question:

How might managers use subjective performance evaluation in this setting?

Answer:

figure 2.6.1 : The line up of AS Roma in season 2000/01

figure 2.6.1 : The line up of AS Roma in season 2000/01

  - Lets refer to https://en.wikipedia.org/wiki/2000%E2%80%9301_A.S._Roma_season to observe the top performance of AS Roma in season 2000/01. Gabriel Batistuta, Vincenzo Montella and Francesco Totti are the main three spiritual partners who lead the team to be final winner.
  
  - The website http://www.zonalmarking.net/2010/02/09/teams-of-the-decade-10-roma-2000-01/ has analyse the secret of winning in season 2000/01:-
  
    + The real reason Roma became title winners was because others stepped up and became truly top-class players. Vincent Candela went from being an average left-back to a rampaging wing-back, Damiano Tomassi and Cristiano Zanetti had the seasons of their careers, and Francesco Totti became truly world-class.
    
    + Against a 4-4-2, this side worked brilliantly. The three centre-backs marked the opposition forwards with a man to spare, the Roma 4 sat deeper than the opposition 4 in midfield, and negated their ability to counter. Totti played inbetween the lines – with two strikers upfront, the opposition could only mark him with a holding midfielder, which then created room for Tomassi or Zanetti. It did leave the opposition full-backs free, but they were effectively playing against two full-backs playing high up the pitch (Cafu and Candela) who were both defensively very aware.
    
    + The three-man defence worked because if one wing-back got bypassed on the flank, the centre-back closest to him was comfortable covering in a wide area, and the wing-back on the opposite side would tuck in, to make a back four. So if Candela got beaten on the overlap, Samuel would come to meet the winger, Aldair/Zago and Zebina would cover in the centre, and Cafu would defend the back post.
    
    + The only real debate in this side concerned Batistuta’s partner. Marco Delvecchio was the tall, gangly targetman who rarely scored but supposedly did a great job for the team; Vincenzo Montella was the small, pacey poacher with an incredible scoring record.
    
  - Overall, when we talk about a manager going to evaluate a winning team, definitely the teamwork and the tacit understanding are the most crucial reason, as well as the ability and the adequate position and line up of the team. Tacit understanding among team members are very subjective since when a stricker is attacking and the other players will automatically get a best position to coordinate with him. Once passing the ball will shooting, heading or dribbling plus shooting. A team with all famous and strong players might not as strong as a team cooperates with tacit understanding.

3. Conclusion

figure 3.1: Italian soccer club AS Roma and Captain Francesco Totti.

figure 3.1: Italian soccer club AS Roma and Captain Francesco Totti.

4. Appendices

4.1 Documenting File Creation

It’s useful to record some information about how your file was created.

[1] “2016-08-08 03:59:15 JST” setting value
version R version 3.3.1 (2016-06-21) system x86_64, mingw32
ui RTerm
language (EN)
collate English_United States.1252
tz Asia/Tokyo
date 2016-08-08
sysname release version nodename “Windows” “10 x64” “build 10586” “RSTUDIO-SCIBROK” machine login user effective_user “x86-64” “scibr” “scibr” “scibr”

4.2 Versions’ Log

4.3 Speech and Blooper

I do appreciate that University of Illinois at Urbana–Champaign provides the Improving Business Finances and Operations specialization via Coursera. I used to study Certified Accounting Technician (CAT) course at PAAC more more decade. Now I need to review the finance and accounting course prior to conduct my research Analyse the Finance and Stocks Price of Bookmakers.

Author image syui

Operations Management : Module 1 Assignment 2

Operations Management : Module 1 Assignment 2

Improving Business Finances and Operations Specialization by University of Illinois at Urbana-Champaign

®γσ, Eng Lian Hu 白戸則道®

2016-08-28

1. Introduction

Instructions

The purpose of this assignment is to give you the opportunity to apply the concepts you have learned in this module and to discuss some of the key ideas of the module in your own words. Follow the instructions provided and respond to each question. This a required activity for this module.

Submit your answers to each of the questions based on the information provided below. Enter your answers directly in the spaces provided in the My submission tab. You may save a draft of your work as you go, and you can come back later to continue working on your draft. When you are finished working, click the Preview button, verify your identity, and then click Submit for Review to submit your assignment. Please answer each question fully and concisely.

The discussion of the assignment solution is provided in the Module 1 Assignment 2 Solution video. Do the assignment on your own first, before viewing the assignment discussion video!

Module 1 Assignment 2

Following are the relevant figures extracted from the balance sheet and income statement of two companies, a consumer electronics manufacturer and a large retailer.

Category Consumer.Electronics Large.Retailer
Sales $108,249 $446,950
Earnings $ 25,922 $ 15,699
Assets $116,371 $193,406
Equity $ 76,615 $ 75,761

Table 1.1 : Comparison of relevant information of balance sheet and income statement from two companies.

2. Operational Concepts

2.1 Compute the asset turnover for each company.

Category Consumer.Electronics Large.Retailer
Sales $108,249 $446,950
Assets $116,371 $193,406
Asset Turnover 93.02% 231.09%

Table 2.1 : Comparison of Asset-Turnover of two companies.

What is ‘Asset Turnover Ratio’?

Asset turnover ratio is the ratio of the value of a company’s sales or revenues generated relative to the value of its assets. The Asset Turnover ratio can often be used as an indicator of the efficiency with which a company is deploying its assets in generating revenue.

\(Asset Turnover = Sales or Revenues / Total Assets\)

Generally speaking, the higher the asset turnover ratio, the better the company is performing, since higher ratios imply that the company is generating more revenue per dollar of assets. Yet, this ratio can vary widely from one industry to the next. As such, considering the asset turnover ratios of an energy company and a telecommunications company will not make for an accurate comparison. Comparisons are only meaningful when they are made for different companies within the same sector.

Read more: Asset Turnover Definition | Investopedia

2.2 Compute the operating margin for each company.

Category Consumer.Electronics Large.Retailer
Earnings $ 25,922 $ 15,699
Sales $108,249 $446,950
Operating Margin 23.95% 3.51%

Table 2.2 : Comparison of Operating-Margin of two companies.

What is an ‘Operating Margin’?

Operating margin is a margin ratio used to measure a company’s pricing strategy and operating efficiency.

Operating margin is a measurement of what proportion of a company’s revenue is left over after paying for variable costs of production such as wages, raw materials, etc. It can be calculated by dividing a company’s operating income (also known as operating profit) during a given period by its net sales during the same period. Operating income here refers to the profit that a company retains after removing operating expenses (such as cost of goods sold and wages) and depreciation. Net sales here refers to the total value of sales minus the value of returned goods, allowances for damaged and missing goods, and discount sales.

Operating margin is expressed as a percentage, and the formula for calculating operating margin can be represented in the following way:

\(Operating Margin = Operating Income / Net Sales\)

Operating margin is also often known as operating profit margin, operating income margin, return on sales or as net profit margin. However, net profit margin may be misleading in this case because it is more frequently used to refer to another ratio, net margin.

Read more: Operating Margin Definition | Investopedia

2.3 Compute the return on equity for each company.

Category Consumer.Electronics Large.Retailer
Earnings $ 25,922 $ 15,699
Equity $ 76,615 $ 75,761
Return of Equity 33.83% 20.72%

Table 2.3 : Comparison of Return-On-Equity of two companies.

What is ‘Return On Equity - ROE’?

Return on equity (ROE) is the amount of net income returned as a percentage of shareholders equity. Return on equity measures a corporation’s profitability by revealing how much profit a company generates with the money shareholders have invested.

ROE is expressed as a percentage and calculated as:

\(Return on Equity = Net Income/Shareholder's Equity\)

Net income is for the full fiscal year (before dividends paid to common stock holders but after dividends to preferred stock.) Shareholder’s equity does not include preferred shares.

Also known as return on net worth (RONW).

Read more: Return On Equity (ROE) Definition | Investopedia

2.4 What does your analysis suggest about the differences in operations performance of the two companies?

Category Consumer.Electronics Large.Retailer
Asset Turnover 93.02% 231.09%
Operating Margin 23.95% 3.51%
Return of Equity 33.83% 20.72%

Table 2.4 : Comparison of Operations Performance of two companies.

We can compare the companies above to know that :-

Case Study :

I used to work as a customer service operator in Ladbrokes Far East Asian department (Scicom MSC Bhd) and now I’ve affiliate business partnership with Ladbrokes and some other companies. From my personal view, I try to separate the digital business and brick-and-mortar retailing outlet of Ladbokes as example. I assume that Consumer Electronic is digital business operates around the World while Large Retailer is the outlets which operates within Europe.

  1. Asset Turnover >>>
  • The asset of digital subsidiary company or department is smaller since there has just only server and some IT related staffs as well as a centralized customer support department needed. I try to assume that only 300 staffs for digital business.
  • The asset of retailer outlet or department is larger since every single brick-and-mortar outlet required staffs, property and also fixed expenses. The number of staff for retailer is extremely higher which might probably more than 10,000 staffs.
  1. Operating margin >>>
  • The net profit generates by digital department is higher due to low flexible cost for wages, rentals etc.
  1. Return on Equity >>>
  • The return of investment on digital business is higher than retailer business. Which means every single unit of shares that investors invest on Ladbrokes via stock market has generate higher return/dividend from the portion of digital business.

3. Conclusion

There has only few importance figures took into counting in this assignment. If both balance sheet and income statement of a company is not faud, the operational perforamce might reflect the healthiness of a company. We/Investors can easily know the potential of growth/profitable, if the company is overvalued or undervalued and if it is worth or valued to invest their fund.

There are a lot of figure that has not been states while it can be analysed and know the intrinsic value which is always quote and measure by Warren Buffet. - Warren Buffett: How He Does It? - Buffett’s Value Formula (?) - How does Warren Buffett value a business?

4. Appendices

4.1 Documenting File Creation

It’s useful to record some information about how your file was created.

[1] “2016-08-28 13:12:18 JST” setting value
version R version 3.3.1 (2016-06-21) system x86_64, mingw32
ui RTerm
language (EN)
collate English_United States.1252
tz Asia/Tokyo
date 2016-08-28
sysname release version nodename “Windows” “10 x64” “build 10586” “RSTUDIO-SCIBROK” machine login user effective_user “x86-64” “scibr” “scibr” “scibr”

4.2 Versions’ Log

4.3 Speech and Blooper

Same as pevious assignment — Operations Management : Module 1 Assignment 1, I do appreciate that University of Illinois at Urbana–Champaign provides the management course via Coursera. I like reading the legend of business tycoons (for example: Konosuke Matsushita, Peter Drucker, Bill Gates, Warrent Buffet, George Soros, Jim Rogers, Lee Kah Sheng, Henry Fok Ying Tung, Peter Lynch, Lim Goh Tong etc) to know how was their mindset and business strategy since I was a computer science student in Tunku Abdul Rahman College. I used to read the legend of Warren Buffet and then started my journey in financial market before join sportsbook industry.

Author image syui

Betting Strategy and Ⓜodel Validation - Part II

Betting Strategy and Ⓜodel Validation - Part II

Betting Model Analysis on Sportsbook Consultancy Firm A

®γσ, Eng Lian Hu 白戸則道®

2016-09-23

Abstract

This is an academic research by apply R statistics analysis to an agency A of an existing betting consultancy firm A. According to the Dixon and Pope (2004)1 Kindly refer to 24th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References, due to business confidential and privacy I am also using agency A and firm A in this paper. The purpose of the anaysis is measure the staking model of the firm A. For more sample which using R for Soccer Betting see http://rpubs.com/englianhu. Here is the references of rmarkdown and An Introduction to R Markdown. You are welcome to read the Tony Hirst (2014)2 Kindly refer to 1st paper in Reference for technical research on programming and coding portion for the paper. in 7.4 References if you are getting interest to write a data analysis on Sports-book.

1. Introduction to the Betting Stategics

2. Data

3. Summarise the Staking Model

4. Staking Ⓜodel

4.1 Basic Equation

Before we start modelling, we look at the summary of investment return rates.

table 4.1.1 : 5 x 5 : Return of annually investment summary table.3 Kindly refer to the list of colors via Dark yellow with hexadecimal color code #9b870c for plot the stylist table.

\[\Re = \sum_{i=1}^{n}\rho_{i}^{EM}/\sum_{i=1}^{n}\rho_{i}^{BK} \cdots equation 4.1.1\]

\(\Re\) is the return rates of investment. The \(\rho_i^{EM}\) is the estimated probabilities which is the calculated by firm A from match 1,2… until \(n\) matches while \(\rho_{i}^{BK}\) is the net/pure probability (real odds) offer by bookmakers after we fit the equation 4.1.2 into equation 4.1.1.

\[\rho_i = P_i^{Lay} / (P_i^{Back} + P_i^{Lay}) \cdots equation 4.1.2\]

\(P_i^{Back}\) and \(P_i^{Lay}\) is the backed and layed fair price offer by bookmakers.

We can simply apply equation above to get the value \(\Re\). From the table above we know that the EMPrice calculated by firm A invested at a threshold edge (price greater) 1.0769894, 1.1072203, 1.0781056, 1.1148426, 1.0671108 than the prices offer by bookmakers. There are some description about \(\Re\) on Dixon and Coles (1996)4 Kindly refer to 25th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References. The optimal value of \(\rho_{i}\) (rEMProbB) will be calculated based on bootstrapping/resampling method in section 4.3 Kelly Ⓜodel.

table 4.1.2 : 48640 x 45 : Odds price and probabilities sample table.

Above table list a part of sample odds prices and probabilities of soccer match \(i\) while \(n\) indicates the number of soccer matches. We can know the values rEMProbB, netProbB and so forth.

graph 4.1.1 : A sample graph about the relationship between the investmental probabilities -vs- bookmakers’ probabilities.

Graph above shows the probabilities calculated by firm A to back against real probabilities offered by bookmakers over 48640 soccer matches.

Now we look at the result of the soccer matches.

table 4.1.3 : 7 x 8 : Summary of betting results.

The table above summarize the stakes and return on soccer matches result. Well, below table list the handicaps placed by firm A on agency A. I list the handicap prior to test the coefficient according to the handicap in next section 4.2 Linear Ⓜodel.

table 4.1.4 : 6 x 8 : The handicap in sample data.

4.2 Linear Ⓜodel

From our understanding of staking, the covariates we need to consider should be only odds price since the handicap’s covariate has settled according to different handicap of EMOdds.

Again, I don’t pretend to know the correct Ⓜodel, here I simply apply linear model to retrieve the value of EMOdds derived from stakes. The purpose of measure the edge overcame bookmakers’ vigorish is to know the levarage of the staking activities onto 1 unit edge of odds price by firm A to agency A.

table 4.2.1 : Summary of linear models.

table 4.2.2 : Anova of linear models.

When I used to work in 188Bet and Singbet as well as AS3388, we know from the experience which is the odds price of favorite team win will be the standard reference and the draw odds will adjust a little bit while the underdog team will be ignore.

Steven Xu (2013)5 Kindly refer to 16th paper in Reference for industry knowdelege and academic research portion for the paper. has do a case study on the comparison of the efficiency of opening and closing price of NFL and College American Football Leagues and get to know the closing price is more efficient and accurate compare to opening price nowadays compare to years 1980~1990. It might be due to multi-million dollars of stakes from informed traders or smart punters to tune up the closing price to be likelihood.

In order to test the empirical clichés, I used to conduct a research thoroughly through ®γσ, Eng Lian Hu (2016)6 Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References, I completed the research on year 2010 but write the thesis in year 2016. and concludes that the opening price of Asian Handicap and also Goal Lines of 29 bookmakers are efficient than mine. However in my later ®γσ, Eng Lian Hu (2014)7 Kindly refer to 4th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References applied Kelly staking model where made a return of more than 30% per sesson. Meanwhile, the Dixon and Coles (1996) and Crowder, Dixon, Ledford and Robinson (2001)8 Kindly refer to 27th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References has built two models which compare the accuracy of home win, draw and away win. From a normal Poison model reported the home win is more accurate and therefore an add-hoc inflated parameter required in order to increase the accuracy of prediction. You are feel free to learn about the Dixon and Coles (1996) in section 4.4 Poisson Ⓜodel.

Kindly click on regressionApps to use the ShinyApp

Kindly click on regressionApps to use the ShinyApp

shinyapp 4.2.1 : Summary and anova of linear models.

Based on table 2.2.1 we know about the net bookies probabilities and EM probabilities, here I simply apply linear regression model9 You can learn from Linear Regression in R (R Tutorial 5.1 to 5.11). You can also refer to Getting Started with Mixed Effect Models in R, A very basic tutorial for performing linear mixed effects analyses and Fitting Linear Mixed-Effects Models using lme4. Otherwise you can read Linear Models with R and somemore details about regression models via Extending the Linear Model with R : Generalized Linear, Mixed Effects and Nonparametric Regression Models. Besides, What statistical analysis should I use? summarise a table for test analysis and data validation. and also anova to compare among the models.

You might select Y response variable and X explanatory variable(s) to measure your model10 Refer to Shiny height-weight example for further information about shinyapp for linear models. or existing models.

Kindly click on regressionApps to use the ShinyApp

Kindly click on regressionApps to use the ShinyApp

shinyapp 4.2.2 : Comparison of the vigorish between AH and Fixed-Odds. Source from 1x2 to Combo AH version 1.1 by William Chen (2006)

Here I simply attached with a Fixed Odds to Asian Handicap’s calculator which refer to my ex-colleague William Chen’s11 My ex-colleague and best friend in sportsbook industry which known since join sportsbook industry year 2005 —— Telebiz and later Caspo Inc. spreadsheet version 1.1 in year 2006. You can simply input the home win, draw, away win (in decimal format) as well as the overround to get the conversion result from the simple an basic equation.12 Kindly refer to my previous research to know the vigorish / overround.

John Fingleton & Patrick Waldron (1999) apply Shin’s model and finally conclude suggests that bookmakers in Ireland are infinitely risk-averse and balance their books. The authors cannot distinguish between inside information and operating costs, merely concluding that combined they account for up to 3.7% of turnover while normally Asian bookmakers made less than 1% and a anonymous company has made around 2%. However the revenue or the stakes are farly more than European bookmakers.13 You can refer to my another project Analyse the Finance and Stocks Price of Bookmakers which analysis the financial report of public listed companies and also profitable products’ revenue and profit & loss of anonymous company..

They compare different versions of our model, using data from races in Ireland in 1993. The authors’ empirical results can be summarised as follows:

  • They reject the hypothesis that bookmakers behave in a risk neutral manner;
  • They cannot reject the hypothesis that they are infinitely riskaverse;
  • They estimate gross margins to be up to 4 per cent of total oncourse turnover; and
  • They estimate that 3.1 to 3.7% (by value) of all bets are placed by punters with inside information.

Due to the Shin model inside the paper research for the sake of bookmakers and this sportsbook consultancy firm is indeed the informed trading (means smart punters or actuarial hedge fund but not ordinary gambler place bets with luck). Here I think of test our previous data in paper ®γσ, Eng Lian Hu (2016)14 Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References which collect the dataset of opening and also closing odds price of 40 bookmakers and 29 among them with Asian Handicap and Goal Line. Meanwhile, there has another research on smart punters (Punters Account Review (Agenda).xlsx) which make million dollars profit from Ladbrokes. You are feel free to browse over the dataset for the paper. and also the anonymous companies’s revenue and P&L to analyse the portion of smart punters among the customers in Analyse the Finance and Stocks Price of Bookmakers. However the betslip of every single bet require to analyse it. The sparkR amd RHadoop as well as noSQL require in order to analyse the multiple millions bets. It is interesting to analyse the threaten of hedge fund15 Kindly refer to 富传奇色彩的博彩狙击公司EM2 to know the history and the threaten of EM2 sportsbook consultancy company to World wide known bankers. since there has a anonymous brand among the brands under Caspo Inc had closed due to a lot of smart punters’ stakes and made loss. Well, here I leave it for future research16 Here I put in 6.2 Future Works. if the dataset is available.

4.3 Kelly Ⓜodel

From the papers Niko Marttinen (2001)17 Kindly refer to 1th paper in Reference for industry knowdelege and academic research portion for the paper. and Jeffrey Alan Logan Snyder (2013)18 Kindly refer to 2nd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References both applying Full-Kelly,Half-Kelly and also Quarter-Kelly models which similar with my previous Kelly-Criterion model ®γσ, Eng Lian Hu 201419 Kindly refer to 4th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References but enhanced.

To achieve the level of profitable betting, one must develop a correct money management procedure. The aim for a punter is to maximize the winnings and minimize the losses. If the punter is capable of predicting accurate probabilities for each match, the Edward O. Thorp (2006)20 Kindly refer to 6th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References has proven to work effectively in betting. It was named after an American economist John Kelly (1956)21 Kindly refer to 26th paper in Reference for industry knowdelege and academic research portion for the paper. in 7.4 References and originally designed for information transmission. The Kelly criterion is described below:

\[S=(\rho*\sigma-1)/(\sigma-1) \cdots equation 4.3.1\]

Where S = the stake expressed as a fraction of one’s total bankroll, \(\rho\) = probability of an event to take place, \(\sigma\) = odds for an event offered by the bookmaker. Three important properties, mentioned by Hausch and Ziemba (1994) (Efficiency of Racetrack Betting Markets (2008Edition)), arise when using this criterion to determine a proper stake for each bet:

  • It maximizes the asymptotic growth rate of capital
  • Asymptotically, it minimizes the expected time to reach a specified goal
  • It outperforms in the long run any other essentially different strategy almost surely

The criterion is known to economists and financial theorists by names such as the geometric mean maximizing portfolio strategy, the growth-optimal strategy, the capital growth criterion, etc. We will now show that Kelly betting will maximize the expected log utility for sports-book betting.

[1] 23.71528

\[K = \frac{(B + 1)p - 1} {B} \cdots equation 4.3.1\]

\[G: = \mathop {\lim }\limits_{N \to \infty } \frac{1/N}{\log}\left( {\frac{{{BR_N}}}{{{BR_0}}}} \right) \cdots equation 4.3.2\]

\[BR_N = (1 + K)^W(1 - K)^L BR_0 \cdots equation 4.3.3\]

Kelly K-value 凯利模式资金管理

## Bootstrapping to get the optimal value
#'@ llply(rEMProbB)

table 4.3.2

In order to get the optimal value, I apply the bootrapping and resampling method.

\[L(\rho) = \prod_{i=1}^{n} (x_{i}|\rho) \cdots equation 4.3.4\]

Now we look at abpve function from a different perspective by considering the observed values \(x1, x2, …, xn\) to be fixed parameters of this function, whereas \(\rho\) will be the function’s variable and allowed to vary freely; this function will be called the likelihood.

4.4 Poisson Ⓜodel

Niko Marttinen (2001)22 Kindly refer to 1th paper in Reference for industry knowdelege and academic research portion for the paper. has enhanced the Dixon and Coles (1996) which are :

  • Basic Poisson model : Independence Poisson model for both home and way teams with a constant home advantage parameter.
  • Independent home advantages model : Seperate the home advantage parameter depends on the teams accordingly.
  • Split season model : Split a soccer league season to be 1st half and 2nd half season.
    1. Scores plus Poisson model.

From above models, the author has compare the efficiency and the best fit model for scores prediction as below.

figure 4.4.1 : Comparison of various Poison models.

figure 4.4.1 : Comparison of various Poison models.

From figure 4.4.1 above, the author compare the deviance of the models23 Kindly refer to Generalized Linear Models in R, Part 2: Understanding Model Fit in Logistic Regression Output, devianceTest and Use of Deviance Statistics for Comparing Models to learn baout the method of comparison.

  • Weighted model :

Here we introduce the Dixon and Coles (1996) model and its codes. You are freely learning from below links if interest.

table 4.4.1 : Filtered multiple bets placed on same matches.

Due to the soccer matches randomly getting from different leagues, and also not Bernoulli win-lose result but half win-lose etc as we see from above. Besides, there were mixed Pre-Games and also In-Play soccer matches and I filter-up the sample data to be 20009 x 45. I don’t pretend to know the correct answer or the model from firm A. However I take a sample presentation Robert Johnson (2011)24 Kindly refer to 23th paper in 7.4 References from one of consultancy firm which is Dixon-Coles model and omitted the scoring process section.

Here I cannot reverse computing from barely \(\rho_i^{EM}\) without know the \(\lambda_{ij}\) and \(\gamma\) values. Therefore I try to using both Home and Away Scores to simulate and test to get the maximum likelihood \(\rho_i^{EM}\).

\[X_{ij} = pois(\gamma \alpha_{ij} \beta_{ij} ); Y_{ij} = pois(\alpha_{ij} \beta_{ij}) \cdots equation 4.4.1\]

sample…

In order to minimzie the risk, I tried to validate the odds price range invested by firm A.25 As I used to work in AS3388 which always take bets from Starlizard where they only placed bets within the odds price range from 0.70 ~ -0.70. They are not placed bets on all odds price in same edge. The sportbook consulatancy firms will not place same amount of stakes on same edge, lets take example as below :-

  • \(Odds_{em}\) = 0.40 while \(Odds_{BK}\) = 0.50, The edge to firm will be 0.5 ÷ 0.4 = 1.25
  • \(Odds_{em}\) = 0.64 while \(Odds_{BK}\) = 0.80, The edge to firm will be 0.8 ÷ 0.64 = 1.25

We know above edge is same but due to the probability of occurance an event/goal at 0.4 is smaller than 0.64. Here I try to bootstrap/resampling the scores of matches of the dataset and apply maximum likelihood on the poisson model to test the Kelly model and get the mean/likelihood value. Boostrapping the scores and staking model will be falling in the following sections [4.5 Staking Ⓜodel and Ⓜoney Management] and 4.6 Expectation Ⓜaximization and Staking Simulation.

4.5 Staking Ⓜodel and Ⓜoney Ⓜanagement

Section : reverse modelling to get the EMProb prior to calculate the coefficient of the staking model. Otherwise might rearrange the order of applied Poison model here by refer to international competitions.

Galema, Plantinga and Scholtens (2008)26 You are feel free to refer to Reference for industry knowdelege and academic research portion for the paper. in 7.4 References for further details

reminder (temporary noted for further):

draft : 
  - http://www.moneychimp.com/articles/risk/regression.htm
  - read *Galema, Plantinga and Scholtens (2008)* https://englianhu.files.wordpress.com/2016/06/the-stocks-at-stake-return-and-risk-in-socially-responsible-investment.pdf
  - reverse engineering on staking-profit linear regression model to get/retrieve EMProb value since now only get the coefficients figire of EMProb. Although incompleted soccer teams... 2ndly, reversed poison model from EMProb might is not workable on one-sided competition, need to refer to some international competition as references for incompleted dataset.

Martin Spann and Bernd Skiera (2009)27 Kindly refer to 19th paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References applied a basic probability sets on the draw games and also the portion of win and loss. The author simply measured the portion of the draw result with win/loss to get the edge to place a bet. However it made a loss on Italian operator Oddset due to the 25% high vigorish but profitable in 12%. Secondly, the bets placed on fixed odds but not Asian Handicap and also a fixed amount $100.

sample… Geometric Mean

Parimutuel Betting

4.6 Expectation Ⓜaximization and Staking Simulation

sample…

5. ®esult

  • Section 5.1 Comparison of the ®esults - Comparison of the Returns of Staking Models.
  • Section [5.2 Ⓜarket Basket] - Analyse the Hedging or Double up Invest by Firm A.

5.1 Comparison of the ®esults

Chapter 4.2 Comparison of Different Feature Sets and Betting Strategies in

Dixon and Pope (2003) apply linear model to compare the efficiency of the odds prices offer by first three largest Firm A, B and C in UK.

5.2 Market Basket

Here I apply the arules and arulesViz packages to analyse the market basket of the bets.

6. Conclusion

6.1 Conclusion

Due to the data-sets I collected just one among all agents among couple sports-bookmakers 4lowin. Here I cannot determine if the sample data among the population…

JA : What skills and academic training (example: college courses) are valuable to sports statisticians?

KW : I would say there are three sets of skills you need to be a successful sports statistician:

  • Quantitative skills - the statistical and mathematical techniques you’ll use to make sense of the data. Most kinds of coursework you’d find in an applied statistics program will be helpful. Regression methods, hypothesis testing, confidence intervals, inference, probability, ANOVA, multivariate analysis, linear and logistic models, clustering, time series, and data mining/machine learning would all be applicable. I’d include in this category designing charts, graphs, and other data visualizations to help present and communicate results.
  • Technical skills - learning one or more statistical software systems such as R/S-PLUS, SAS, SPSS, Stata, Matlab, etc. will give you the tools to apply quantitative skills in practice. Beyond that, the more self-reliant you are at extracting and manipulating your data directly, the more quickly you can explore your data and test ideas. So being adept with the technology you’re likely to encounter will help tremendously. Most of the information you’d be dealing with in sports statistics would be in a database, so learning SQL or another query language is important. In addition, mastering advanced spreadsheet skills such as pivot tables, macros, scripting, and chart customization would be useful.
  • Domain knowledge - truly understanding the sport you want to analyze professionally is critical to being successful. Knowing the rules of the game; studying how front offices operate; finding out how players are recruited, developed, and evaluated; and even just learning the jargon used within the industry will help you integrate into the organization. You’ll come to understand what problems are important to the GM and other decisionmakers, as well as what information is available, how it’s collected, what it means, and what its limitations are. Also, I recommend keeping up with the discussions in your sport’s analytic community so you know about the latest developments and what’s considered the state of the art in the public sphere. One of the great things about being a sports statistician is getting to follow your favorite websites and blogs as a legitimate part of your job!

source : Preparing for a Career as a Sports Statistician: Two Interviews with People in the Field

… … …

6.2 Future Works

Niko Marttinen (2001) has conducted a very detail and useful but also applicable betting system in real life. There has a ordered probit model which shows a high accuracy predictive model compare to his Poisson (Escore) model. Well, the ®γσ, Lian Hu ENG (2016)28 The research modelling with testing the efficiency of odds price which had completed in year 2010. Kindly refer to 3rd paper in Reference for industry knowdelege and academic research portion for the paper. under 7.4 References has build a weight inflated diagonal poisson model which is more complicated and shophitiscated and later ®γσ, Lian Hu ENG (2014)29 Kindly refer to 4th paper inside Reference for industry knowdelege and academic research portion for the paper. under 7.4 References. However there has an automatically and systematically trading system which wrote in VBA + S-Plus + Excel + SQL30 the betting system has stated in his paper. which is very useful as reference. The author use VBA to automac the algorithmic trading while there has no Asian Handicap and Goal Line odds price data to simulate compare to mine. While currently the shinyapps with RStudioConnect can also build an algorithmic trading system. However the session timeout issue31 The connection timeout issue might be a big issue for real time algorithmic trading might need to consider. The shinydashboard example from ｮStudio might probably cope with the issue.

John Fingleton & Patrick Waldron (1999) applied Shin model to test the portion of hedge funds and smart punters. As I stated in 4.2 Linear Ⓜodel, the sparkR, RHadoop and noSQL require in order to analyse the high volume betslips dataset. Its interesting and will conduct the research if all betslips of bookmaker(s) is(are) available in the future.

I will be apply Shiny to write a dynamic website to utilise the function as web based apps. I am currently conducting another research on Analyse the Finance and Stocks Price of Bookmakers which is an analysis on the public listed companies and also anonymous companies revenue and profit & loss. You are welcome to refer SHOW ME SHINY and build your own shinyapps.

I will also write as a package to easier load and log.

7. Appendices

7.1 Documenting File Creation

It’s useful to record some information about how your file was created.

  • File creation date: 2015-07-22
  • File latest updated date: 2016-09-23
  • R version 3.3.1 (2016-06-21)
  • R version (short form): 3.3.1
  • rmarkdown package version: 1.0.9014
  • tufte package version: 0.2.2
  • File version: 1.0.0
  • Author Profile: ®γσ, Eng Lian Hu
  • GitHub: Source Code
  • Additional session information

[1] “2016-09-23 23:27:52 JST”

7.2 Versions’ Log

  • File pre-release version: 0.9.0
    • file created
    • Applied ggplot2, ggthemes, directlabels packages for ploting. For example, the graphs applied in Section [2. Data].
  • File pre-release version: 0.9.1
    • Added Natural Language Analysis which is research for teams’ name filtering purpose.
    • Changed from knitr::kable to use datatble from DT::datatable to make the tables be dynamic.
    • Changed from ggplot2 relevant packages to googleVis package to make graph dynamic.
    • Completed chapter [3. Summarise the Staking Model].
  • File pre-release version: 0.9.2 - “2016-02-20 09:41:49 JST”
  • File pre-release version: 0.9.3 - “2016-02-05 05:24:35 EST”
    • Modified DT::datatable to make the documents can be save as xls/csv
    • Added log file for version upgraded
  • File pre-release version: 0.9.3.1 - 2016-06-22 13:36:33 JST
    • Reviewed previous version, DT::datatable updated new version replaced Button extension from TableTools, removed sparkline and htmlwidget
    • Applied linear regression to test the efficiency of staking model by consultancy firm A

7.3 Speech and Blooper

Firstly I do appreciate those who shade me a light on my research. Meanwhile I do happy and learn from the research.

Due to the rmarkdown file has quite some sections and titles, you might expand or collapse the codes by refer to Code Folding and Sections for easier reading.

There are quite some errors when I knit HTML:

  • let say always stuck (which is not response and consider as completed) at 29%. I tried couple times while sometimes prompt me different errors (upgrade Droplet to larger RAM memory space doesn’t helps) and eventually apply rm() and gc() to remove the object after use and also clear the memory space.

  • Need to reload the package suppressAll(library('networkD3')) which in chunk decission-tree-A prior to apply function simpleNetwork while I load it in chunk libs at the beginning of the section 1. Otherwise cannot found that particlar function.

  • The rCharts::rPlot() works fine if run in chunk, but error when knit the rmarkdown file. Raised an issue : Error : rCharts::rPlot() in rmarkdown file.

  • xtable always shows LaTeX output but not table. Raised a question in COS : 求助！knitr Rmd pdf 中文编译 2016年8月19日 下午9:56 7 楼.Here I try other packages like textreg and stargazer. You can refer to Test version to view the output of stargazer function and the source codes I reserved but added eval = FALSE in chunks named lm-summary and lm-anova to unexecute the codes.

  • I refer to R Shiny: Rendering summary.ivreg output and tried to plot the output table, but there has no bottom statistical information like Residual standard error, Degree of Freedom, R-Squared, F-statistical value and also p-value, therefore I use R Shiny App for Linear Regression, Issue with Render Functions which simply renderPrint() the verbatimTextOutput() in shinyapp 4.2.1.

  • I tried to raise an issue about post the shinyapps to RStudioConnect at Unable publish to RStudio Connect : Error in yaml::yaml.load(enc2utf8(string), …) : Reader error: control characters are not allowed: #81 at 276 #115. You might try to refer to the gif files in #issue 115 for further information. I tried couple times and find the solution but there has no an effective solution and only allowed post to ｮPubs.com where I finally decide to seperate the dynamic shinyApp into another web url.

  • Remark : When I rewrite Report with ShinyApps : Linear Regression Analysis on Odds Price of Stakes and would like to post to ｮStudioConnect, the wizard only allowed me post to rPubs.com (but everyone know rPubs only allow static document which is not effort to support Shinyapp). Therefore kindly refer to https://beta.rstudioconnect.com/content/1766/. You might download and run locally due to web base version always affected by wizards and sometimes only view datatable but sometimes only can view googleVis while sometimes unable access.

  • I am currently work as a customer service operator and self research as a smart punter. Hope to setup my sportsbook hedge fund company website Scibrokes® and running business and back to the sportsbook betting industry soon…

Terminator II

Terminator II

7.4 References

Reference for industry knowdelege and academic research portion for the paper.

  1. Creating a Profitable Betting Strategy for Football by Using Statistical Modelling by Niko Marttinen (2006)
  2. What Actually Wins Soccer Matches: Prediction of the 2011-2012 Premier League for Fun and Profit by Jeffrey Alan Logan Snyder (2013)
  3. Odds Modelling and Testing Inefficiency of Sports Bookmakers : Rmodel by ®γσ, Eng Lian Hu (2016)
  4. Apply Kelly-Criterion on English Soccer 2011/12 to 2012/13 by ®γσ, Eng Lian Hu (2014)
  5. The Betting Machine by Martin Belgau Ellefsrød (2013)
  6. The Kelly Criterion in Blackjack Sports Betting, and the Stock Market by Edward Thorp (2016)
  7. Statistical Methodology for Profitable Sports Gambling by Fabián Enrique Moya (2012)
  8. How to apply the Kelly criterion when expected return may be negative? by user1443 (2011)
  9. Money Management Using The Kelly Criterion by Justin Kuepper
  10. Optimal Exchange Betting Strategy For WIN-DRAW-LOSS Markets by Darren O’Shaughnessy (2012)
  11. Kelly criterion with more than two outcomes by David Speyer (2014)
  12. 凯利模式资金管理 by Chung-Han Hsieh (2015)
  13. Optimal Determination of Bookmakers’ Betting Odds: Theory and Tests by John Fingleton & Patrick Waldron (1999)
  14. Optimal Pricing in the Online Betting Market by Maurizio Montone (2015)
  15. Why are Gambling Markets Organised so Differently from Financial Markets? by Steven Levitt (2004)
  16. Forecasting Accuracy and Line Changes in the NFL and College Football Betting Markets by Steven Xu (2013)
  17. The Forecast Ability of the Dispersion of Bookmaker Odds by Kwinten Derave (2013-2014)
  18. The Stocks at Stake: Return and Risk in Socially Responsible Investment by Galema, Plantinga and Scholtens (2008)
  19. A Comparison of the Forecast Accuracy of Prediction Markets, Betting Odds and Tipsters by Martin Spann and Bernd Skiera (2009)
  20. Efficiency of the Market for Racetrack Betting by Donald Hausch, William Ziemba and Mark Rubinstein (1981)
  21. Betting Market Efficient at Premiere Racetracks by Marshall Gramm (2011)
  22. Late Money and Betting Market Efficiency: Evidence from Australia by Marshall Gramm, Nicholas McKinney and Randall Parker (2012)
  23. An introduction to football modelling at Smartodds by Robert Johnson (2011)
  24. The Value of Statistical Forecasts in the UK Association Football Betting Market by Dixon and Pope (2003)
  25. Modelling Association Football Scores and Inefficiencies in the Football Betting Market by Dixon & Coles (1996)
  26. A New Interpretation of Information Rate by John Kelly (1956)
  27. Dynamic Modelling and Prediction of English Football League Matches for Betting by Crowder, Dixon, Ledford and Robinson (2001)

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